Geometry
Unit 3 Review Sheet
Name: _____________________________
I can prove that triangles are congruent using valid theorems/postulates. (G-CO.8)
1.
What congruence shortcuts can you use to prove that triangles are congruent?
List all 5 of the methods.
2.
For each of the following triangles, determine which theorem/postulate could be used to show that
the triangles are congruent. If they are congruent, write a congruence statement, if there is not enough
information, explain why you cannot prove the triangle congruent.
Triangles:
Are these triangles If the triangles are congruent,
Don’t forget to mark additional sides/angles which
Congruent? By
write a congruence statement.
are congruent!
which theorem or If the triangles are NOT
postulate?
congruent, explain why they are
not congruent.
I can prove that triangles are congruent using valid theorems/postulates. (G-CO.8)
3. Suppose PQ  AB and QS  BC . What is needed to prove PQS  ABC by each method?
Draw two triangles representing this situation.
What additional information
is needed to prove congruent
by SSS?
We would need
What additional information
is needed to prove congruent
by SAS?
We would need
4. Complete the following proof.
Statements
Justifications
1.
1. Given
2.
4.
2. Alternate interior angles are
congruent.
3. Alternate interior angles are
congruent.
4. Given
5. ABC  EDC
5.
3.
I can use the definition of congruent triangles and corresponding parts to solve problems. (G-CO.7)
5. Given that  LMN   PQR, complete the following congruence statements:
L  _____
MN  ____
R  _____
PR  ____
6. In an isosceles triangle PQR, PQ  QR , the measure of the vertex angle is (4x + 10) The measure of each
base angle is (2x - 5).
a. Draw an isosceles triangle and label each angle with the
given information
b. Write an equation and solve for x.
c. Find the measure of each base angle.
d) Find the measure of the vertex angle.
7. Given: NEW  YAR . Let mE  (14 x  4) , mY  (3x  7) and mW  75
Draw and label both
triangles to the right.
List all six pairs of
corresponding
congruent parts
Write an equation to
solve for x.
I can prove theorems about triangles and use these theorems to solve problems.(G-CO.10)
8. Complete the proof.
Given: A  C ; BD bisects ABC
Statements
1.
Justifications
Given
2.
Given
3.
Definition of angle bisector
Prove: ABD  CBD
B
A
D
C
4.
5. ABD  CBD
I can prove theorems about triangles and use these theorems to solve problems.(G-CO.10)
9. Find all the missing angle measures in the diagram shown.
ma=_______
mh=_______
mb=_______
mk=_______
mc=_______
mm=_______
md=_______
mp=_______
me=_______
mr=_______
mf=_______
ms=_______
mg=_______
mb=___________
mc=___________
md=___________
me=___________