Download 1.1 Building Blocks of Geometry

1.1 Building Blocks of Geometry
Name
Definition
Picture
Short Rorm
Point
A location in space
Line
An infinite number of points
extending in two directions. A
line only has length.
TM
Ray
An infinite number of points in
a straight line from a given
point.
TM
Line Segment
An infinite number of points in
a straight line between two
given points.
Plane
A flat surface that extends
outward forever with length
and width, but no thickness.
The point P
M
T
Collinear
points
Points on the same line
Coplanar
points
Points on the same plane
Angle
Two noncollinear rays sharing
the same endpoint form an
angle
Endpoints
A terminating or starting
point of a ray, line segment,
or arc
TM
T
P
M
D
Just say it
Just say it
BHM or
MHB or H
Just say it
1. Name each picture using the proper notation/symbols. If you can name the picture more than
one way, then do so.
P
B
B
A
Q
H
M
T
M
2. Draw RA , HB , g , and a plane containing the points JML.
3. For the following picture is the notation B a good idea? Why? P
H
M
B
4. Use your ruler to measure the following segment in cm and then in inches and write it in the
form mAB =
A
B
5. How many points define a line, a plane?
1.2 Pool Room Math.
1. Label each angle with a letter and measure the angles using a protractor. Write your answers
in the form mA 
Congruence is where two shapes have the exact same size and shape. The symbol is
Congruent segments have the exact same measure.
Congruent angles have the exact same measure.
*Numbers are EQUAL.
*Shapes are CONGRUENT
mA  mB
A  B
Labeling angles and segments
mA  35

mAEB  120
A
B

mCED  80 
E
CE  6
AB  5
EB  3
C
D
Showing congruent segments and angles.
A
A  B
C  D
AE  BE
CE  DE
AB  CD

B
E
C
D
What would be wrong with using the notation E ?
Mark the following on the given shape.
A  B
C  D
AB  AE
CE  BE
DB  CD
A
mC  90 
mAEB  60 
mCEB  90 
CE  6
AB  10
B
E
EB  7
C
D

1.3 Conditionals, Converse, Counterexample, and more definitions.
Conditional- A sentence with a condition and then a result. Usually in the form of :
If x  3  4 , then x  1
If it rained, then the street is wet.
What do these statements all have in common?

If an mA  90 , then A is a right angle.
If a polygon is a square, then it is a rhombus
1. Write a conditional.
Converse- The reverse statement.
If x  1, then x  3  4
If the street is wet, then it rained.
What did I do to the previous statements to create these?
If A is a right angle , then the mA  90
If a polygon is a rhombus, then it is a square
2. Write the converse to your conditional.
Biconditional- A statement where the conditional and the converse are true and written using "if and only if."
Examples.
If x  3  4 , then x  1 ,
If x  1, then x  3  4
x  3  4 if and only if x  1
If an mA  90 , then A is a right angle.
If A is a right angle , then the mA  90
A is a right angle if and only if the mA  90
3. Can you write a biconditional using your conditional and converse? If not true, then try writing one using
another scenario.
Counterexample- An example that makes something not true. It counteracts the statement.
4. Given the conditional: If it rained, then the street is wet.
a) Write the converse.
b) Give a counterexample to disprove the converse.
5. Given the conditional: If x  3 , then x 2  9
a) Write the converse.
b) Give a counterexample to disprove the converse.
Name
Picture (give a
measurement)
Definition
An angle with a measure
of 90 deg.
An angle with a
measure of less than 90
deg.
An angle with a
measure of more than
90 deg.
Right Angle
Acute angle
obtuse angles
Midpoint of a
segment
The point equidistant
from both endpoints
The line segement
equidistand from the
segments creating the
angle
Angle bisector
6. Mark each figure to indicate the given information. Use the congruent slashes and symbol for a right angle.
a)
AB = CD, mA mD
b) Point F is the midpoint of sAC, CDB is a right angle,
and sAE is an angle bisector.
C
B
A
C
E
F
D
.
A
D
B
Defining line and angle relationships.
Name
Definition
Picture (give a
measurement)
Short Form
l
Parallel lines
Two or more lines that
lie in the same plane
and do not intersect
Perpendicular lines
Two lines that lie in the
same plane and
intersect at a 90 degree
angle.
Pair of
complementary
angles
Two angle whose
measures have a sum of
90 degrees.
Pair of
supplementary
angles
Two angle whose
measures have a sum of
180 degrees.
Pair of vertical
angles
Two nonadjacent
angles formed by two
intersecting lines
Linear pair of angles
A pair of angles that
form a line.
m
m
lm
m p
p
Draw and carefully label the following:
1. Two vertical angles 1 and 2
2. PE  AR
3.
4. Supplementary angles D and F with mD  35
PE ET
Name
Picture
Definition
1.4
Defining POLYGONS (many knees)
Polygon-- A closed figure in a plane, formed by a finite set of non collinear line segments.
Sides
Name
Sides
Name
Sides
2
6
10
3
7
11
4
8
12
5
9
p
Name
Definition
Convex polygon
A polygon where no segments
connecting any two vertices can
be drawn outside the polygon.
Concave polygon
A polygon were at least one
segment connecting two
vertices can be drawn outside
the polygon
Consecutive vertices
Two vertices connected by a
side.
Consecutive sides
Two sides that share a vertice
Consecutive angles
Two angles that share a side
Congruent polygons
Polygons where all
corresponding sides have equal
measures and all corresponding
angles have equal measures.
Name
Picture
Diagonal
A segment connecting two
nonconsecutive vertices
Equilateral Polygon
A polygon where all sides are
equal.
Equiangular polygon
A polygon where all angles are
equal.
Regular polygon
A polygon where all sides are
equal and all angles are equal
Draw and carefully label the following: Use a ruler and protractor.
1. Hexagon HEXGON with right G and diagonal sEO
3. Draw a Hexagon ABCDEF where A  D  F .
2. Equiangular quadrilateral QUAD.
1.5 Triangles
Name
Definition
Picture
Right triangle
A triangle with one right angle
A triangle where all angles are
acute.
Acute triangle
Obtuse triangle
A triangle with one obtuse angle
Scalene triangle
A triangle where no sides are
equal
Isosceles triangle
A triangle with at least two
congruent sides
Equilateral triangle
A triangle where all sides are
congruent
Median of a triangle
A segment connecting the
midpoint of a side to the
opposite vertex
Altitude of a triangle
A perpendicular segment from
the vertex to the opposite side
or the line containing the
opposite side.
Draw and carefully label the following:
1. An obtuse scalene triangle
2. Triangle ABC with median AE.
3. Acute triangle DEF with altitude DA
4. Obtuse triangle MOP, mO  130 , with altitude ME.
1.6 Quadrilaterals
Name
Definition
Trapezoid
A Quadrilateral with exactly on pair of
parallel sides
Kite
A Quadrilateral with exactly two pairs of
distinct congruent consecutive sides
Parallelogram
A Quadrilateral with two pair of parallel
sides.
Rhombus
An equilateral Quadrilateral
Rectangle
An equiangular Quadrilateral
Square
Picture
An equiangular and equilateral
Quadrilateral
QUADRILATERALS
TRAPEZOIDS
PARALLELOGRAMS
RHOMBUS
KITES
RECTANGLE
SQUARE
Use your geometric tools to draw and label each figure. These must be close to exact.
9.
Isosceles right triangle ABC with right angle B
10.
Trapezoid ZOID with sZO // sID,
mOZD = 75°, and mZOI = 45°
Exercises--Group work---Review. Answer the following questions.
Match each statement from 1 to 8 with a letter from the box.
1.
2.
3.
4.
5.
6.
7.
8.
a. Decagon
b. Isosceles
c. Scalene
e. Acute
f. Octagon
g. Hexagon
i. Collinear
j. Coplanar
k. Protractor
m. AB
n. AB
o. 

d. Obtuse
h. Dodecagon
l. 
p. 
_______
_______
_______
_______
_______
_______
_______
_______
BA
AB
AB
The tool used to measure angles in degrees
Three or more points on a line
A triangle with all sides of unequal measure
A triangle with at least two sides of equal measure
A ray starting at point B and passing through point A
A line segment with endpoints A and B
An angle whose measure is greater than 90°
A polygon with ten sides
Match each statement from 1 to 8 with a letter from the box.
a. Rhombus
e. Angle bisector
i. Parallel
b. Rectangle
f. Median
j. Supplementary
c. Trapezoid
g. Altitude
k. Complementary
d. Parallelogram
h. Perpendicular bisector
1.
2.
3.
4.
5.
6.
_______
_______
_______
_______
_______
_______
7.
_______
8.
_______
Two angles whose measures add up to 180°
Two lines in the same plane that do not intersect
An equiangular parallelogram
A quadrilateral with exactly one pair of parallel sides
An equilateral quadrilateral
A segment in a triangle connecting a vertex with the
midpoint of the opposite side
A segment in a triangle from a vertex perpendicular to
the line containing the opposite side
A segment in a triangle from a vertex to the opposite
side dividing the angle into two parts of equal measure
9. True or False. If false, then give a counterexample or reason why it is false.
a) _____An angle bisector divides an angle into two congruent angles.
b) _____If two lines intersect then they form a right angle.
c) _____Every square is a rectangle.
d)_____Every square is a rhombus.
e)_____An obtuse triangle has exactly one angle greater than 90 degrees
1.7 Circles
Circle- The set of points in a plane equidistant form a given point(the center of the circle).
radius- A segment from the center of the circle to a point on the circle
(the distance from the center to a point on the circle.)
Congruent Circles- two circles with the same radius.
Concentric circles - Two circles with the same center
Arc of a circle- part of a circle
Semicircle- An arc that is half the circle
Minor Arc- less than half the circle Major Arc- more than half
Chord- a segment connecting two points on the circle.
Diameter- a cord containing the center of the circle.
Secant line- a line that intersects two or more points of a circle or curve.
Tangent line- a line that intersects one and only one point on the object.
Inscribed angle- An angle created by two different cords sharing a point on the circle.
Central angle- an angle with vertex at the center of the circle
1.8 Space Geometry
Let's do some drawing.
Cylinder
Cone
Prism
Sphere
1. Draw a rectangular solid 3 cm by 4 cm by 5 cm, resting on its smallest face.
Pyramid
Hemisphere
1.9 If you can't picture it then DRAW A PICTURE.
1.
David is 3 years older than Stephen and 2 years younger than Graham. If Neil is 4 years younger than
Graham, how much older than Neil is David? ____________
2
The box on the right is wrapped with two strips of ribbon as shown. What length of ribbon was needed to
decorate the box? Break the box down into it's six sides.
3. At one point in a race, Homer was 25 feet behind Bart and 28 feet ahead of Marge. Marge was trailing Lisa
by 40 feet. Who is winning the race and by how much? How much is Homer losing the race by?
Locus- a set of points/dots. Planes can be paper, cardboard, or any flat surface.
4. Line AB lies in a plane. Sketch the locus of points in that plane that are 3 cm from line AB. Sketch the
locus of points in the space that are 3 cm from line AB. What shapes do the locus of points make for each
sketch?
5. Point P lies in the plane. Sketch the locus of points in that plane that are 3 cm from the point P. What shape
do the locus of points make?