Download 1 - Collingswood High School

1.2
Points, Lines, and Planes
definition-
undefined terms-
points-
line-
plane-
collinear points-
coplanar points-
a. Name three points that are collinear.
b. Name four points that are coplanar.
c. Name three points that are not collinear.
Term
Line
Line segment
Definition
Symbol
Picture
Ray
Opposite rays
endpointsinitial point-
GEOMETRIC DRAWING…
-Draw 3 noncollinear points J, K, L
-Then draw
-Then draw
-Last draw
-Draw the intersection of a plane and a line.
-Draw the intersection of two planes.
-Draw two points, A and B. Then sketch AB. Add point C on the segment between A
and B.
⃗⃗⃗⃗⃗ , ⃡⃗⃗⃗⃗
-Draw points A, B, C, D, E, with no three collinear. Then sketch ̅̅̅̅
𝐴𝐵 , 𝐵𝐶
𝐶𝐷, ̅̅̅̅
𝐷𝐸 , ⃗⃗⃗⃗⃗
𝐴𝐸
Together...
1) The three undefined terms of geometry are
________________________________________.
2) Lines intersect at a ____________________.
3) Planes intersect at a ___________________.
4) How do we represent line AB? _______________
5) How do we refer to the line segment AB? ______________
6) Points that lie on the same line are called _______________________.
C
A
D
E
F
7) Name 2 planes that intersect at line AD. ______________________
8) Are points C, E, F and A coplanar? ______________________
9) Name the 4th point that is coplanar with points C, E, and F. _______
1.3
Segments and Their Measures
distance-
length-
between-
The Ruler Postulate
A
B
C
D
E
F
G
-3
-2
-1
0
1
2
3
Segment Addition Postulate-
EX 2 (a) XY= 12
(b)
MN=3
EX 3
AB=x
BC= x+6
AC=24
Find:
YZ=4 XZ= ________
OP= 18 MP=31
NO=_______
B is between A and C
x= ______
AB=______
BC= ______
Ex. 4
Q is between T and W
TQ=2x+3
TW= 22
QW=x+4
Find: x= ________
TQ= ________
QW= _______
Segment bisectorMidpoint-
congruent segments-
Sketch the 3 collinear points. Then write the Segment Addition Postulate for the
points.
e. A is between P and L
f. R is between T and G
Ex. 5 Q is the midpoint of PR. What are PG, QR, and PR if PQ = 6x – 7 and
QR = 5x + 1
In the diagram, AE = 20, BD = 6, and AB = BC = CD. Find each length.
j. BC
n. CD
k. AB
o. DE
l. CA
p. BE
m. DA
q. CE
1.4
Measuring Angles
anglesidevertex-
NAMING ANGLES
Angles that have the same measure are called
.
*Lengths are equal.
Segments are congruent.*
*Measures are equal.
Angles are congruent.*
Angle Addition Postulate
Example: Solve for x.
155°
12
m<1 = 4x-20
m<2 = 3x +14
CLASSIFYING ANGLES
acute
right
obtuse
straight
Classify the angle.
a. m A = 180º
c. m
C = 90º
b. m
d. m
D = 34º
B = 106º
Use the diagram to answer the questions.
e. Is
ABD
DBE?
f. Is
DBA
EBC?
g. Are
DBE and
EBC adjacent?
h. Are
ABD and
CBE adjacent?
Name the vertex and sides of the angle. Then estimate its measure.
1.5
Angle Pair Relationships
Adjacent angles-
vertical angles-
linear pair-
Ex. 1
a) Identify all vertical angles
b) Identify all linear pairs
c) Identify adjacent angles
1
3
2
4
Vertical angle measures…
Linear pair measures…
Ex. 2
Angle 5 has a measure of 56º, what are the measures of the other 3 angles?
5
Ex. 3
6
8
7
Solve for x and y. Then give the measures of the four angles.
(y + 20) º
(3x +5) º
(4y – 15) º (x + 15) º
Complementary Angles-
Supplementary Angles-
Ex. 4 Complementary or Supplementary? Adjacent or nonadjacent?
a.
b.
c.
d.
Ex. 5
Ex. 6
Ex. 7
A is complementary to B, which is supplementary to
what are the measures of A and B?
D is complementary to E and supplementary to
are the measures of the other two angles?
C. If m A is 76º,
F. If m E is 34º, what
Find x and y, and then find the measures of all four angles.
(3x + 20) º
yº
(5x – 50) º
Angle bisector-
1.7
Distance and Midpoint
Midpoint Formula
Find the coordinates of the midpoint.
a. (1, 2) and (3, 6)
b. (-3, -5) and (-7, 10)
The midpoint of AB is C. Use the coordinates of A and C to find the coordinates of
B.
c. A (3, 4) and C (7,8)
d. A(-4,0) and C (0,-2)
Find the coordinates of the midpoints.
g. B(7,6) M(-5, 4)
h. A(0,0) B(-8,6)
Find the coordinates of the other endpoints of a segment with the given endpoint
and midpoint M.
i. D(-2, -4) M(5, -4)
j. Q(4,2) M(7,3)
Distance Formula-
Find the distance between the two points.
a. (1, 2) and (4, 6)
b. (-2, -3) and (0, 0)
Use the distance formula to determine if JK
KL
h. J (3, -5)
i. J (0, -8)
K (-1, 2)
K (4, 3)
L (-5, -5
L (-2, -7)
c. (1,-3) and (-4,2)