Download Unit 1B: Congruence and Similarity Name MATH 8 STUDY GUIDE

Unit 1B: Congruence and Similarity
MATH 8 STUDY GUIDE
Name ___________________________________
Period _______ Date ____________
Knowledge: Draw a picture to assist you if needed. Write answers on a separate piece of notebook paper.
1.
2.
3.
4.
5.
Which transformations are congruent to the original figure? Translation, Rotations and Reflections Which are similar to the
original figure? Dilations
How many angles are formed when a transversal intersects 2 parallel lines? 8 anglers How many different angle measures will
there be? Two different measures – one will be acute and one will be obtuse
Name and draw a picture to show each special angle pair created when 2 parallel lines are cut by a transversal (there are 5
special angle pairs). Alternate Interior, Alternate Exterior, Corresponding Angles, Same-side Interior, Same-side Exterior
What is the sum of the interior angles of any triangle?180 degrees
What is the sum of the exterior angles of any triangle? 360 degrees What is the relationship between an exterior angle of a
triangle and the 2 opposite interior angles? The exterior angles is the sum of the two non-adjacent (remote) interior angles.
Dilation:
6.
Draw a dilation of the figure using the scale
factor of ¼. Name the new coordinates.
7. Draw a dilation of the figure using the scale factor
of 2. Name the new coordinates.
A’ (0,1) B’ (1,-1) C’ (-1, -1)
A’ (4,0), B’ (0,-4), C’ (-4, 2),
D’ ( 2, 4)
Parallel Lines Cut by a Transversal:
8. Given: m || n. What is the m 2 ? _85_________
9. Given: PQ RS . What is m∡1.
_115_______
(b) Name the relationship between the angles?
__Corresponding Angles_____________________________
65
P
85
m
R
S
1
2
n
10. Using the figure to the right, name a pair of angles that are:
a) Alternate interior _3,6 and 4,5_______________
b) Alternate exterior _1,8 and 2, 7________________
c) Same-side exterior _1,7 and 2,8_________________
d) Vertical 1,4 2,3 5,8 6, 7________________________
e) Same-side interior _3,5 and 4,6______________
f) Supplementary 1,2 2,4 3,4 1,3 6,8 8,7, 7,5 5,6_______________
93°
1
3
5
7
6
8
Q
2
4
g) Corresponding _1,5 3,7 2,6 4,8______________
Triangle Angles
11. Find the missing measure.
12. Find the measure of angle a. Explain how you
found it.
39
102
33
a
45
63°
78°
13. Solve for the given variable.
14.
160
If Marietta had the following 5 roads with
the given miles, how many miles would “x” be?
3 miles
2 miles
6 miles
15. Find the measure if the missing angle.
X=9
x miles
16. Determine if the triangles are similar. Solve for a.
The missing angle measures 40
3 a

5 15
a9
140˚
x + 60
17. Based on these triangles being similar, find
find the scale factor of the smaller triangle to the
Larger triangle.
6
18. Based on the similar triangles below, find the missing
angle.
14
7
The scale factor is 2
3 x

2 20
2 x  60
x  30