Review Chapter 4-Congruent Triangles
Name ___________________________
Complete the following:
1.
What parts of an equiangular triangle are equal?
2.
If corresponding parts of triangles are congruent, what relationship do the triangles have?
3.
The 3 angles of any triangle sum to what number?
4.
What is the measure of each angle in an equiangular triangle?
5.
What are the equal sides of an isosceles triangle called?
6.
What is the exterior angle theorem?
7.
What are 3 ways to classify triangles by angles?
8.
What is an included angle?
9. From the information given, determine the correct congruent name of the other
triangle.
∆CAB  ∆ _______________
10.
∆XGH  ∆ _______________
Name the congruent angles and sides for each pair of congruent triangles.
a.) ∆TUV  ∆XYZ
b.) ∆CDG  ∆RSW
Angles:
Angles:
Sides:
Sides:
11. In the diagram below, ∆MKL  ∆JET. Use the triangles to complete the following
statements.
a.) L  __________
b.) MK  __________
c.) mM  __________
d.) mT  __________
e.) ∆ETJ  __________
12. Decide whether you can use the SSS, SAS, ASA Postulate or the AAS Theorem to prove
the triangles congruent. If so, write the congruence statement, and identify the postulate or
theorem. If not, write not possible.
a.)
b.)
c.)
d.)
e.)
f.)
13. In the diagram below, B is a point on AC such that  ADB is an equilateral triangle, and
 DBC is an isosceles triangle with DB  BC . Find m∠C.
14. Write the correct triangle congruence statement for each pair of marked triangles.
T
Y
W
Q
R
X
M
N
E
C
D
15. Given the congruence statement, label the triangles correctly:
JKL  CAB
16. Using the congruence statement QRS  FGH , find mG
S
H
400
Q
300
R
F
G
17.
18. In the diagram below, m∠A = x, m∠B = 2x + 15 and m∠ACD = 5x + 5. What is m∠B?
19. In the diagram below, B is a point on AC such that  ADB is an equilateral triangle, and
 DBC is an isosceles triangle with DB  BC . Find m∠C.
D
A
B
C
20. Find the slope of a line perpendicular to the line whose equation is 2y – 6x = 4.
21.
22. What is the equation used to find the midpoint between 2 points?
23.
a) Find the midpoint between (3, -2) and (4, -5) using the formula above (show all work)
b) If I wanted to find a location between your house and the school, would I use midpoint or
distance?
R
Complete the 2 column proof:
24.
Given : CS  AC
BC  CR
Prove: RSC  BAC
C
A
_____________Statements
1.
CS  AC
25.
Given : AB // CD
BC  CR
S
B
Reasons__________________
1. Given
C
B
mABC  mCDA
Prove: CBD  ADB
A
_____________Statements
1. AB // CD
mABC  mCDA
Reasons__________________
1.
Given
D
N
26. Given : LM  NM
O
O is the midpoint of LN
Prove: NMO  LMO
L
M
_____________Statements
1.
LM  NM
Reasons__________________
O is the midpoint of LN
1. Given
X
27.
Given : RS  XY
WY  QR
Q
Prove: SRQ  XYW
S
R
_____________Statements
1.
RS  XY
WY  QR
W
Reasons__________________
1. Given
Y
28.