Download What is it? How do you draw it? How do you write or name it? Draw

Point
What is it?
An undefined term thought of as a location with no size or
dimension. It is the most basic building block of geometry.
What is it?
How do you draw it?
How do you write or name it?
Draw point D.
How do you draw it?
A dot with a capital letter.
How do you write or name it?
A capital letter. (Ie. point D.)
Draw point D.
You need the dot and the
capital letter near it.
D
Section 1.1
SJS
Page 1
line
What is it?
An undefined term thought of as a straight, continuous
arrangement of infinitely many points extending forever in
two directions. A line has length, but no width or thickness,
so it is one-dimensional.
What is it?
How do you draw it?
How do you write or name it?
Draw and name line NE.
How do you draw it?
A straight line with arrows at each end.
How do you write or name it?
Any two points on the line with a line symbol above it.
or a lower case letter written near the arrow.
Draw and name line NE.
Check for arrows and the two
points with labels near the points.
NE
or
EN
N
E
(Because, it’s the same set of points!)
Make sure a line (with arrows) is above the capital letters.
Section 1.1
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Page 2
plane
What is it?
How do you draw it?
What is it?
An undefined term thought of as a flat surface that extends
infinitely along its edges. A plane has length and width but no
thickness, so it is two-dimensional.
How do you draw it?
A 4-sided figure slanted to give it perspective.
How do you write or name it?
Draw plane PLN.
How do you write or name it?
A capital script (or cursive) letter, near a corner.
Or with any three points in the plane that are not collinear.
Draw plane PLN.
Make sure the points are inside the parallelogram that you
drew. (You could use a rectangle too, but a parallelogram gives
dimension.) Even though a plane does not have edges, you need to draw it
somehow.
L
N
P
Section 1.1
SJS
Page 3
Mixed up stuff
Give all possible names for the line:
Give all possible names for the line:
C
L
t
C
A
L
t
A
CL , LC , AL , LA , AC , CA
or just t.
Give all possible names for the plane.
Give all possible names for the plane.
R
A
R
X
Plane PAX, AXP, XPA,
XAP, PAX, or APX
or Plane R .
A
X
P
P
Section 1.1
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Page 4
collinear
Define it.
Points on the same line.
Define it.
Draw collinear points D, O, and G.
Draw collinear points D, O, and G.
Make sure all three points are on a line (with arrows).
Or you could have any part
G
of a line (a segment or ray), but
O
a line is better.
D
Draw non-collinear points C, A, and T.
Make sure any one of the three points are not “in line” with
the other two points. (Note: Any two points make a line.)
or
Draw non-collinear points C, A, and T.
C
T
A
T
C
A
Section 1.1
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Page 5
coplanar
Define it.
Define it.
Points (or other figures) in the same plane.
E
Draw coplanar points M, A, and T.
Then illustrate that points T, E, A, and M
are non-coplanar.
Draw coplanar lines n and m. Name the plane that
contains them P.
Draw coplanar points M, A, and T.
Then illustrate that points
T, E, A, and M are non-coplanar.
M
A
T
(M, A and T must be within the boundary, but E must be obviously outside
the boundary.)
Draw coplanar lines n and m. Name the plane that
contains them P.
(Eventhough a plane does not
have edges, the arrows on the
lines should be inside the
boundary, the lower case letters
should be near the arrows and the
P should be in a corner.)
P
m
n
Section 1.1
SJS
Page 6
ray
Define it.
A part of a line that starts at one point, called the endpoint, and
extends infinitely through another point.
Define it.
Draw and write ray RA.
Draw and write ray RA.
RA
Give all possible names for the ray:
A
(the only name possible)
R
C
A
B
Give all possible names for the ray:
BA or BC
C
are the only 2 names.
The endpoint must be first!
A
B
Section 1.1
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Page 7
Line segment
Define it. Use the word endpoint in your definition.
A part of a line that consists of two points called endpoints
and all of the collinear points between them.
Define it. Use the word endpoint in your definition.
Draw and give all possible names for segment ME.
Draw and give all possible names for segment ME.
Draw a segment AN congruent to segment ME.
Show 3 different ways to write that the segments
are equal in length, that they are congruent.
M
E
ME and EM
(are the same segment!)
Draw a segment AN congruent to segment ME. Show 3
different ways to write that the segments are equal in
length, that they are congruent.
Make sure there are matching
tic marks on the segments!
E
M
A
N
mME  mAN , ME  AN , ME  AN
Section 1.1
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Page 8
Measure of line segments
What type of units do you use to measure segments with?
Inches, feet, millimeters, centimeters, etc ...
What type of units do you use to measure segments
with?
Draw and label segment NA that measures 4.3 cm.
(Check this with your ruler and label with 4.3 cm.)
Draw and label segment NA that measures 4.3 cm.
4.3 cm
N
A
(The drawing above it is NOT to scale!)
Show 2 different ways to write that the segment
you drew measures 4.3 cm.
Show 2 different ways to write that the segment you drew
measures 4.3 cm.
NA  4.3 cm , mNA  4.3 cm
Section 1.1
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Page 9
Midpoint [of a segment]
Define it.
A point on a segment that is the same distance from both
endpoints.
Define it.
OR A point that divides the segment into two congruent
segments.
Draw and label A the midpoint of NP .
Draw and label A the midpoint of NP .
Make sure there are matching
P
tic marks on each side of A!
A
N
Show 3 different ways to write that the midpoint
gives you equal (or congruent) segments.
Show 3 different ways to write that the midpoint gives you
equal (or congruent) segments.
mNA  mAP , NA  AP , NA  AP
Section 1.1
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Page 10
Bisect
Define it.
Means to cut into two equal parts
Define it.
Make sure there are matching
Draw “point A bisects segment PN”.
Draw “ray AR bisects angle BAN”. Then show 2
different ways to write the equal (or congruent)
angles.
P
Draw “point A bisects segment PN”.
tic marks on each side of A.
A
N
Draw “ray AR bisects angle BAN”. Then show 2 different
ways to write the equal (or congruent) angles.
B
Make sure there are matching
arc marks and tic marks on each side of AR .
R
A
N
mBAR  mRAN
BAR  RAN
Draw “ray AR bisects segment NB”.
R
Draw “ray AR bisects segment NB”.
N
Section 1.1
SJS
A
Page 11
B
Angle
Define it (as well as side and vertex).
Name all of the angles in the drawing along with
their measures. Make sure you use the correct
notation.
Define it.
An angle is a figure formed by two rays with a common
endpoint.
The two rays are the sides of the angle, and the common
endpoint is the vertex.
Name all of the angles in the
drawing along with their
measures. Make sure you
use the correct notation.
mLOM  71 , mNOM  69 , mLON  140
Note: You CAN’T say
mO
because there are three possible angles!
Section 1.2
SJS
Page 12
Angle bisector
Define it.
A ray that contains the vertex of the angle and divides the angle
into two congruent angles.
Define it.
Name all of the angle bisectors in the drawing. Use
the correct notation! Also explain why.
Name all of the angle bisectors in the drawing. Use the
correct notation! Also explain why.
UR bisects QUS because
mQUR  mRUS
US bisects RUT because
TUS  RUS
Note: there are various ways to write these
statements correctly!
Check to make sure your statements are correct.
Section 1.2
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Page 13
Adjacent angles.
Define it.
Two angles that share a vertex, share a side, and they share no
interior points (they don’t overlap).
Define it.
Name all of the pairs of adjacent angles in the drawing.
Name all of the pairs of adjacent angles in the
drawing. There are 4 pairs!
D
B
R
DAB is adjacent to BAR ,
BAR is adjacent to RAN ,
DAR is adjacent to RAN ,
BAN is adjacent to BAD
Note: If you use different names for
the angles above, it is still correct.
D
B
R
A
N
Check angles carefully!
A
N
Do adjacent angles need to be congruent?
Do adjacent angles need to be congruent?
NO, but adjacent angles may be congruent, but don’t have to be
congruent.
Section 1.2
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Page 14
Parallel lines
Define it.
Lines (or parts of lines) in the same plane that never intersect.
Define it.
D
Draw line AB parallel to line CD.
C
Make sure you use matching arrow symbols
A
to indicate parallel.
Draw line AB parallel to line CD.
B
How do you write it?
How do you write it?
AB CD
Show how to mark the parallelogram pictured to
illustrate that the opposite sides are parallel.
P
L
A
R
Show how to mark the parallelogram pictured to illustrate
that the opposite sides are parallel.
Make sure you use matching arrow symbols
to indicate parallel.
P
L
A
R
Section 1.3
SJS
Page 15
Skew lines
Define it.
Lines that are not coplanar and never intersect.
p
Define it.
Draw line p and line q are skew.
(Use the plane to emphasize that
q
they’re not coplanar.)
Draw line p and line q are skew.
What is the difference between skew and parallel
lines?
What is the difference between skew and parallel lines?
They both never intersect; however, parallel lines are coplanar
where as skew lines are non-coplanar.
Point out line segments around the room that are
parallel and segments that are skew.
Point out line segments around the room that are parallel
and segments that are skew.
Answers will vary. I.e. any two of the vertical corners of the room you are
in.
Section 1.3
SJS
Page 16
Perpendicular lines
Define it.
Lines (or parts of lines) that intersect at a 90º angle.
Define it.
Draw segment BO is perpendicular to line OG.
Make sure you indicate the 90º angle
Draw segment BO is perpendicular to line OG.
How do you write it?
How do you write it?
B
with the little box in the corner.
O
G
BO  OG
Watch the notation on this!! (Segments don’t have arrows!)
Point out line segments around the room that are
perpendicular.
Point out line segments around the room that are
perpendicular.
Finish the statement with parallel, perpendicular
and/or skew:
If two coplanar lines are perpendicular to the same
line, then they are _____ to each other.
Section 1.3
SJS
Answers will vary.
Finish the statement with parallel, perpendicular and/or
skew:
If two coplanar lines are perpendicular to the same line, then
they are parallel to each other.
Page 17
Acute angle
Define it.
An angle that measures less than 90º (and more than 0º).
Define it.
Draw acute angle ANG. Use the correct notation.
Draw acute angle ANG.
A
(Various: Make sure it is between 0
and 90 degrees.)
44
N
G
Write all possible names for your angle.
Write all possible names for your angle.
Measure your angle. Label your angle with the
measure. How do you write the measure of your
angle?
N , ANG , GNA
(The vertex must be the middle letter!)
Measure your angle. Label your angle with the measure.
How do you write the measure of your angle?
Various: Make sure you are reading the correct degree measure from the
protractor! Make sure the measure is written inside the angle near the
vertex, see above.
Various ways to write the measure, one possible: mN  44
Section 1.3
SJS
Page 18
Obtuse angle
Define it.
An angle that measures more than 90º and less than 180º.
Define it.
Draw obtuse angle OBT.
(Various: Make sure it is between 90
T
136
and 180 degrees.)
B
Draw obtuse angle OBT.
Write all possible names for your angle. Use the
correct notation.
O
Write all possible names for your angle. Use the correct
notation.
B , OBT , TBO
Measure your angle. Label your angle with the measure.
How do you write the measure of your angle?
Measure your angle. Label your angle with the
measure. How do you write the measure of your
angle?
Various: Make sure you are reading the correct degree measure from the
protractor! Make sure the measure is written inside the angle near the
vertex, see above.
Various ways to write the measure, one possible: mB  136
Section 1.3
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Page 19
Right angle
Define it.
An angle that measures exactly 90º.
Define it.
Draw right angle RGT.
R
(Various: Make sure it you indicate 90º with
the square in the corner.)
Draw right angle RGT.
Write all possible names for your angle.
G
T
Write all possible names for your angle.
G , RGT , TGR
The angle is right, so the sides are ___. (word)
The angle is right, so the sides are [perpendicular]. (word)
Show how to write the relationship between the
sides of the angle.
Show how to write the relationship between the sides.
GR  GT
(Both sides should be rays, not segments!)
Section 1.3
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Page 20
Straight angle
Define it.
An angle that measures exactly 180º.
Define it.
Draw straight angle STR.
S
R
T
Draw straight angle STR.
Write all possible names for your angle.
Write all possible names for your angle.
STR , RTS
How many straight
angles are in
the drawing?
Name them. Is there
a problem naming
them?
C
O
B
How many straight angles are in the drawing? Name them.
Is there a problem naming them?
A
C
D
You can name two:
COD, BOA
O
B
A
D
But actually there are 4 (one above and one below each line). The
problem is without an arc mark in the drawing, you have no idea
which straight angle you are talking about.
Section 1.3
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Page 21
Complementary angles
Define it.
Any two angles that add to 90º.
Define it.
Draw non-congruent, adjacent
complementary angles 1 and 2.
Draw non-congruent, adjacent complementary
angles 1 and 2.
What would you need to know to be sure that the
angles are complements? (Write a math
sentence.)
If three angles measure 20º, 30º and 40º are they
complementary? Explain.
Do two angles need to be adjacent to be
complements? Explain.
1
2
(Various, must indicate 90º with the box.
Make sure angle 1 and 2 do not look equal in measure. They do not need to
be equal.)
What would you need to know to be sure that the angles are
complements? (Write a math sentence.)
m1  m2  90
If three angles measure 20º, 30º and 40º are they
complementary? Explain.
No, “complementary” only refers to two angles.
Do two angles need to be adjacent to be complements?
Explain.
No, you could have a 10º angle on one wall and an 80º on
another wall and they would still be considered complementary
(Any 2 angles that add to 90º.)
Section 1.3
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Page 22
Supplementary angles
Define it.
Any two angles that add to 180º.
Define it.
Draw non-congruent, non-adjacent supplementary
angles 3 and 4.
What would you need to know to be sure that the
angles are supplements? (Write a math
sentence.)
Congruent, supplementary angles measure ____
each.
Do two angles need to be adjacent to be
supplements? Explain.
If three angles measure 10º, 100º and 70º are they
supplementary? Explain.
Draw non-congruent,
non-adjacent supplementary
angles 3 and 4. (various)
140˚
3
4 40˚
What would you need to know to be sure that the angles are
supplements? (Write a math sentence.)
m3  m4  180
Congruent, supplementary angles measure 90º each.
Do two angles need to be adjacent to be supplements?
Explain.
No, you could have a 10º angle on one wall and an 170º on
another wall and they would still be considered supplementary
(Any 2 angles that add to 180º.)
If three angles measure 10º, 100º and 70º are they
supplementary? Explain.
No, supplementary only refers to two angles.
Section 1.3
SJS
Page 23
Vertical angles
Define it.
Two non-adjacent angles formed by two intersecting lines.
Draw intersecting lines AB and CD. Label the
intersection O. (Make sure O is between A and B and also
C and D. Name all pairs of vertical angles.)
Define it.
Draw intersecting lines AB and CD. Label the
intersection O. (Make sure O is between A and B
and also C and D.) Name all pairs of vertical
angles.
Name the pairs of
vertical angles.
1
3
2
4
What terms can you use to describe the pair of
angles 3 and  4 , above?
C
Vertical angles
COA and BOD .
COB and AOD .
O
A
D
1
Name the pairs of
vertical angles:
B
3
2
4
1 and 4 , 3 and 2
What terms can you use to describe the pair of angles 3
and  4 above?
They are adjacent and supplementary. And/or they are a linear pair
of angles.
Section 1.3
SJS
Page 24
Linear pair of angles
Define it.
Two adjacent angles formed by a line and a ray.
Define it.
Draw intersecting lines AB and CD. Label the
intersection O. (Make sure O is between A and B and also
C and D.) Name all linear pairs of angles.
Draw intersecting lines AB and CD. Label the
intersection O. (Make sure O is between A and B
and also C and D.) Name all linear pairs of
angles.
Linear pairs of angles are always _____ (a word).
Name all of the
linear pairs
of angles.
1
3
AOC and COB .
COB and BOD .
BOD and DOA .
DOA and AOC .
C
O
A
D
Linear pairs of angles are always _____ (a word).
Supplementary (You can’t say 90º or right. They may not be
congruent!)
2
4
What terms can you use to describe the pair of
angles 3 and  2 ?
B
Name all of the
linear pairs
of angles.
1
3
2
4
1 and 2 , 2 and 4 , 4 and 3 , 3 and 1
What terms can you use to describe the pair of angles
and  2 ?
3
Vertical and congruent both work here.
Section 1.3
SJS
Page 25
Reflex measure of an angle
Define it.
Draw angle LEX with measure 55 degrees. In the
drawing find and label the reflex measure of the
angle.
Define it.
The largest amount of rotation less than 360° from one ray to
another.
Draw angle LEX with measure 55 degrees. In the drawing
find and label the reflex measure of the angle.
L
305
55
E
X
Various: But make sure you label the reflex measure as 305.
Show how you would calculate the reflex measure
of XEL .
Show how you would calculate the reflex measure of
XEL .
360 – 55 = 305
Section 1.3
SJS
Page 26
Polygon
Define it (include side and vertex in your
definition).
Define it (include side and vertex).
A closed figure in a plane, formed by connecting line segments
endpoint to endpoint with each segment intersecting exactly 2
others. Each segment is a side. Each endpoint is a vertex.
E
Draw pentagon PENTA.
Draw pentagon PENTA.
P
N
A
How do you name a polygon? Give another name
for your pentagon above.
How many diagonals does pentagon PENTA have?
Name all of them.
T
How do you name a polygon? The name of the type of
polygon followed by a list of consecutive vertices.
Give another name for your pentagon. (There are many!)
pentagon NTAPE, pentagon NEPAT, pentagon APENT,
etc…
How many diagonals does this pentagon have? Name all of
them.
five diagonals: AE , ET , PN , PT , AN
Section 1.4
SJS
Page 27
Classifying Polygon
Give the names of the different types of polygons (sides
numbering 3 through 12).
Give the names of the different types of polygons
(sides numbering 3 through 12).
How do you name a polygon if you have more than
12 sides?
Sides
3
4
5
6
7
8
9
10
11
12
Name
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Undecagon
Dodecagon
How do you name a polygon if you have more than 12 sides?
Number of sides followed by “-gon”, 13-gon, 100-gon, etc…
If you don’t know the number of sides it’s an n-gon.
Section 1.4
SJS
Page 28
Diagonal
Define it.
A line segment that connects two nonconsecutive vertices.
Define it.
How many diagonals does a triangle have? a quadrilateral?
a pentagon? a hexagon?
triangle: None,
quadrilateral : 2,
pentagon: 5, and
hexagon: 9
How many diagonals does a triangle have?
a quadrilateral? a pentagon? a hexagon?
Name all of the diagonals in the
quadrilateral QUDA.
U
Q
D
A
(Draw them and count them if you need to.)
Name all of the diagonals in the
quadrilateral QUDA.
U
Q
D
QD , UA
A
Section 1.4
SJS
Page 29
Define convex polygon vs. concave polygon.
Convex [polygon] A polygon in which no diagonal is outside
the polygon.
Concave [polygon] A polygon in which at least one diagonal is
outside the polygon.
Define convex polygon vs. concave polygon.
Draw a convex pentagon. Draw a concave pentagon. Show
how each fits their definitions.
E
Draw a convex pentagon. Draw a concave
pentagon. Show how each fits their definitions.
P
P
In the second pentagon,
diagonal PN is outside.
A
A
T
convex
E
P
Draw a convex triangle. Draw a concave triangle.
Any problems?
N
E
N
T
concave
P
R
N
E
A
T
T
Draw a convex triangle. Draw aA concave
triangle.
Any
T
problems?
G
Yup! In this case, there are no diagonals!
R
A triangle is always convex, never concave.
T
Section 1.4
SJS
G
N
Page 30
Congruent
Congruent polygons are polygons with the same [size] and
same [shape].
(Use one word per blank.)
Congruent polygons are polygons with the same
___ and same ___ .
When naming congruent polygons, you must make
sure the ___ vertices are written in the same
order.
Write the congruence shown below.
Use the correct notation!!
When naming congruent polygons, you must make sure the
[corresponding] vertices are written in the same order.
Write the congruence.
Use the correct notation!!
ABC  EFG or CAB  GEF , etc...
The corresponding vertices must match!!
A → E, B → F and C → G.
Also, make sure the congruence symbol is used.
Section 1.4
SJS
Page 31
Congruent
The polygons are congruent.
Copy the polygons and mark
your diagram to show that
C
they are congruent.
The polygons are congruent. Copy the polygons and mark
your diagram to show that they are congruent.
(Check that all of the corresponding parts are marked with the
same number of tic marks.)
E
R
T
Z
N
C
A
How many pairs of parts do you need to mark in
order to show that the polygons are congruent?
Finish the statement, quad. RCTE  _____
E
R
P
T
Z
N
P
A
How many parts do you need to mark in order to show that
the polygons are congruent?
Eight, 4 pairs of sides and 4 pairs of angles.
Finish the statement, quad. RCTE  quad. NZAP
( You must use NZAP, not PAZN or another name, because the corresponding
vertices must match!)
Section 1.4
SJS
Page 32
Congruence
If the quadrilaterals are congruent, show how
to write the congruence statement.
Ie. Quad RCTE  Quad NZPA
If the quadrilaterals
are congruent, show how
to write the congruence
statement.
Make sure the corresponding vertices match up!!
R → N, C → Z, T → P and E → A.
E
R
C
T
Z
N
P
A
How do you write that the corresponding parts that
are congruent? (Write the statements, remember there
How do you write that the corresponding parts that are
congruent? (Write the statements, remember there are
eight.)
C  Z
RE  AN
R  N
RC  ZN
E  A
CT  ZP
T  P
ET  AP
are eight.)
Section 1.4
SJS
Page 33
Equilateral [polygon]
Define it. A polygon with all of its sides equal in length.
Define it.
If possible, draw an equilateral quadrilateral that is
not equiangular.
If possible, draw an equilateral pentagon that is not
equiangular.
(Make sure all figures are marked
with tic marks correctly!)
If possible, draw an equilateral
quadrilateral that is not equiangular.
If possible, draw an equilateral pentagon that is not
equiangular.
If possible, draw an equilateral hexagon that is not
equiangular.
If possible, draw an equilateral hexagon that is not
equiangular.
Section 1.4
SJS
Page 34
Equiangular [polygon]
Define it. A polygon with all of its angles equal in measure.
(Make sure all figures are marked
with tic marks correctly!)
Define it.
If possible, draw an equiangular quadrilateral that
is not equilateral.
If possible, draw an equiangular pentagon that is
not equilateral.
If possible, draw an equiangular hexagon that is
not equilateral.
If possible, draw an equiangular
quadrilateral that is not equilateral.
If possible, draw an equiangular
pentagon that is not equilateral.
Not possible.
If possible, draw an equiangular
hexagon that is not equilateral.
Section 1.4
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Regular [polygon]
Define it. A polygon that is both equilateral and equiangular.
(Make sure all figures are marked with tic marks correctly!)
Define it.
If possible, draw a regular triangular.
If possible, draw a regular triangular.
If possible, draw a regular quadrilateral.
If possible, draw a regular quadrilateral.
If possible, draw a regular pentagon.
If possible, draw a regular pentagon.
If possible, draw a regular hexagon.
If possible, draw a regular hexagon.
Section 1.4
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Perimeter [of a polygon]
Define it. The sum of the lengths of the sides of a polygon.
Define it.
Find the perimeter of
the pentagon.
Find the perimeter of the
pentagon.
Perimeter = 6 + 5 + 5 + 4 + 8
= 28 cm
If the perimeter of a square is 40 inches, how much does
each side measure?
Each side is equal in measure, so 40 ÷ 4 = 10 inches.
If the perimeter of a square is 40 inches, how much
does each side measure?
If one side of a regular hexagon measures 4.5 m,
then its perimeter is?
If one side of a regular hexagon measures 4.5 m, then its
perimeter is?
Each side is equal in measure, so 4.5 * 6 = 27 m
Section 1.4
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Right triangle
Define it. A triangle with one right angle.
(Make sure all figures are marked with tic marks correctly!)
C
Define it.
If possible, draw a right isosceles
B
∆ABC with hypotenuse AC .
If possible, draw a right isosceles ∆ABC with
hypotenuse AC .
If possible, draw a right scalene ∆ABC with right
angle A.
A
If possible, draw a right
scalene ∆ABC with
right angle A.
C
A
B
(Note: no tic marks because no sides are equal.)
If possible, draw an equilateral right ∆ABC with
If possible, draw an equilateral right ∆ABC with
legs AB and AC .
legs AB and AC .
Not possible!
An equilateral triangle is also
equiangular.
Can’t have three 90 degree angles.
OR
If you have a right triangle, the longest side is the hypotenuse
so you can’t have it be equilateral.
Section 1.5
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Acute triangle
Define it. A triangle with three acute angles.
If possible, draw an acute scalene ∆ABC.
Define it.
C
A
(Note: no tic marks because no sides are equal.)
B
If possible, draw an acute scalene ∆ABC.
If possible, draw an acute isosceles ∆ABC with
vertex angle B.
How many angles must be acute before you can
classify a triangle as an acute triangle?
C
If possible, draw an acute
isosceles ∆ABC
with vertex angle B.
A
B
How many angles must be acute before you can classify a
triangle as an acute triangle?
All three must be acute!
Section 1.5
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Obtuse triangle
Define it. A triangle with only one obtuse angle.
Define it.
C
If possible, draw an obtuse isosceles ∆ABC
with legs AB and AC .
A
If possible, draw an obtuse isosceles ∆ABC with
legs AB and AC .
B
If possible, draw an obtuse scalene ∆ABC
with obtuse angle C.
If possible, draw an obtuse scalene ∆ABC with
obtuse angle C.
How many obtuse angles can a triangle have?
C
(Note: no tic marks because no sides are equal.)
B
How many obtuse angles can a triangle have?
Only one.
Section 1.5
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A
Equilateral (or equiangular) triangle
Define each.
An equiangular triangle is a triangle with all angles congruent.
An equilateral triangle is a triangle with all sides congruent.
Define each.
C
If possible, draw an acute
If possible, draw an acute equilateral ∆ABC. If so,
draw it!
Is it possible to draw an equilateral triangle that is
not equiangular? If so, draw it!
equilateral ∆ABC.
B
A
Is it possible to draw an equilateral
triangle that is not equiangular? No.
with triangles, if it is equilateral then
it is equiangular.
Is it possible to draw an equilateral quadrilateral
that is not equiangular? If so, draw it!
Is it possible to draw an equilateral
quadrilateral that is not
equiangular? Yes
Section 1.5
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Scalene triangle
Define it. A triangle with no congruent sides.
Define it.
C
If possible, draw a scalene acute ∆ABC.
A
(Note: no tic marks because no sides are equal.)
If possible, draw a scalene acute ∆ABC.
If possible, draw a scalene right ∆ABC, with right
angle A.
B
If possible, draw a scalene
right ∆ABC, with right angle A.
(Note: no tic marks because no sides are equal.)
C
A
B
If possible, draw a scalene isosceles ∆ABC.
If possible, draw a scalene isosceles ∆ABC.
You can’t! Scalene says no sides equal and for isosceles, you
must have at least two sides equal.
Section 1.5
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Isosceles triangle
Define it. A triangle with at least two congruent sides.
C
Define it.
If possible, draw an isosceles
acute ∆ABC, with base AC.
If possible, draw an isosceles acute ∆ABC, with
base AC.
If possible, draw a right
isosceles ∆ABC, with
right angle A.
A
B
C
A
If possible, draw a right isosceles ∆ABC, with right
angle A.
B
If possible, draw an isosceles equilateral ∆ABC.
Isosceles says you must have at least two sides equal, and a
triangle with 3 sides equal has at least two equal.
(Note: an equilateral/equiangular triangle is a special case of an
isosceles triangle.)
C
If possible, draw an isosceles equilateral ∆ABC.
B
A
Section 1.5
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Quadrilateral
Define quadrilateral. A four-sided polygon.
Define quadrilateral.
A quadrilateral with one pair
of opposite sides parallel
is a [trapezoid].
(Mark the parallel sides with arrows!)
A quadrilateral with one pair of opposite sides
parallel is a _____. Draw it.
A quadrilateral with both
pairs of opposite sides parallel
is a [parallelogram].
A quadrilateral with both pairs of opposite sides
parallel is a _____. Draw it.
A quadrilateral with exactly two distinct pairs of
consecutive congruent sides is a _____. Draw it.
A quadrilateral with exactly
two distinct pairs of
consecutive congruent
sides is a [kite].
Section 1.6
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Parallelogram
Define it. A quadrilateral with both pairs of opposite sides
parallel.
Define it.
An equiangular rhombus is a [square].
An equiangular rhombus is a _____.
An equiangular parallelogram is a [rectangle].
An equiangular parallelogram is a _____.
An equilateral rectangle is a [square].
An equilateral rectangle is a _____.
An equilateral parallelogram is a [rhombus].
An equilateral parallelogram is a _____.
Section 1.6
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Page 45
Quadrilateral Mix Up
Answer with always, sometimes, or never.
Fully explain.
A parallelogram is [sometimes] a square.
A parallelogram could be just a parallelogram, a rectangle, a
rhombus or a square.
A rectangle is [sometimes] a rhombus.
If the rectangle has equal sides (a square), then it is a rhombus.
A parallelogram is _____ a square.
A rectangle is _____ a rhombus.
A square is _____ a rhombus.
A rectangle is _____ a parallelogram.
A parallelogram that is not a rectangle is _____ a
square.
A square is _____ a rectangle.
A square is [always] a rhombus.
A square always has 4 equal sides, so it’s always a rhombus.
A rectangle is [always] a parallelogram.
In a rectangle, both pairs of opposite sides are parallel, so it’s
always a parallelogram.
A parallelogram that is not a rectangle is [never] a square.
You have to have 4 congruent angles to have a square, so if it
isn’t a rectangle, it can’t be a square.
A square is [always] a rectangle.
A square always has 4 congruent angles and it is a
parallelogram, so it must be a type of rectangle.
Section 1.6
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Page 46
Circle
Define it (and center).
Circle is a set of points, a given distance from a given point,
called the center.
Define it (and center).
Draw and label circle A.
A
Draw and label circle A.
Define congruent circles. Draw congruent circles X
and Y.
Define congruent circles. Draw congruent circles X and Y.
Congruent circles are two or more circles with the same radius
measure. (Specify the radii measure.)
Define concentric circles. Draw two concentric
circles with center Z.
Define concentric circles. Draw two concentric circles with
center Z.
Concentric circles are two or
more circles with the
same center point.
Section 1.7
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Circles, segments & lines
Define radius.
A segment that goes from the center to any point on the circle.
Define radius.
Define chord.
A segment connecting any two points on the circle.
Define chord.
Define diameter.
Define tangent & point of tangency.
Define diameter.
A chord that goes through the center of a circle. The largest
chord.
Define tangent.
A line that intersects a circle in only one point.
The point of intersection is called the point of tangency.
Section 1.7
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Circles, segments & lines
A
R
Name all radii.
E
C
P
AP , BP , RP
Name all radii.
Name all chords.
B
A
R
Name all chords.
E
C
D
CD , AB
P
B
D
Name all diameters.
AB
Name all diameters.
Name all tangents & their points of tangency.
Name all tangents & their points of tangency.
BE with point of tangency, B. ER with point of tangency, R.
Section 1.7
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Circles & segment measures.
Define radius (as a distance).
The distance from the center to any point on the circle.
Define radius (as a distance).
Define diameter (in terms of length of radius).
Give two formulas d = ? and r = ?
Define diameter (as a length).
The length of the diameter is two times the radius. d = 2r
or ½ d = r.
If r = 25 inches, then d = ?
d = 2 * 25 = 50 inches
If r = 25 inches, then d = ?
If d = 13 cm, then r = ?
r = 1/2 * 13 = 6.5 or
13
cm
2
If d = 13 cm, then r = ?
Section 1.7
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Arcs
R
A
Give another name for ARB .
Give another name
for ARB .
R
BRA
C
P
B
A
Give all possible names for RBA .
Give all possible
names for RBA .
C
P
B
ABR , RCA or ACR
Name all semicircles.
Name all semicircles.
Must use 3 letters!
Name all minor arcs.
Name all minor arcs.
ARB , ACB
(or equivalent names for these)
Must use 2 letters only! AR , RB , BC , CA , CR
Name all major arcs.
(or equivalent names for these)
Name all major arcs.
Must use 3 letters! Make sure you are not counting the same
arc twice. In other words RBA is the same arc as RCA , so
only list one or the other, not both.
ARC , RBC , RBA , BCR , CAB
(or equivalent names for these)
Section 1.7
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Arcs
Define arc (include endpoints).
Arc [of a circle] is formed by two points on a circle and a
continuous part of the circle between them. The two points are
called endpoints.
Define arc (include endpoints).
Define semicircle.
An arc whose endpoints are the endpoints of the diameter.
Define semicircle.
Define minor arc.
Define major arc.
Define minor arc.
An arc that is smaller than a semicircle. (You use only the
endpoints to name a minor arc.)
Define major arc.
An arc that is larger than a semicircle. (You must use three
points to name a major arc. The endpoint, another point that
the arc passes through, and the other endpoint.)
Section 1.7
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Arcs & angles
Define central angle.
R
A
C
P
If mRPB  43, then mRB 
If mCPB  152, then m AC 
If m ARC  330, then mAPC 
SJS
R
A
C
P
B
B
Define “the measure of an arc”.
Section 1.7
Define central angle
An angle whose vertex
is the center of the circle.
Define “the measure of an arc”
Remember, the arc’s measure is equal to the measure of its
central angle, so
If mRPB  43, then mRB  43.
If mCPB  152, then mAC  28.
180 – 152
If mARC  330, then mAPC  30.
360 – 330
Section 1.7
Page 53
3-D Figures
Sketch a cylinder.
Sketch a cone.
Sketch a sphere.
Sketch a hemisphere.
Sketch a cylinder.
Sketch a cone.
Sketch a sphere.
Sketch a hemisphere.
Note: orientation of the shape on the page does not matter.
Section 1.8
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3-D Figures
Sketch a rectangular prism.
Sketch a square pyramid.
Sketch a triangular pyramid.
Sketch a pentagonal prism.
Sketch a rectangular prism.
Sketch a square pyramid.
Sketch a triangular pyramid.
Sketch a pentagonal prism.
Note: orientation of the shape on the page does not matter.
Section 1.8
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