Geometry TEST REVIEW

Geometry TEST REVIEW
Name ______________________
Period _____ Date ___________
Unit 4 – Congruent Triangles
Triangle Properties (4.1/5.5)
1. All angles of a triangle add up to: ______________
Solve for x: ________
2. The exterior angle measure is equal to the: ______________________________________
Solve for y:
3. Can a triangle have side lengths of 3, 6, and 10? Why or why not? _________________________________
___________________________________________________________________________________________
4. Can the following side lengths form a triangle? State valid or invalid.
Side lengths
4, 5, 8
5, 5, 5
9, 4, 5
4, 10, 5
Valid or invalid triangle?
5. If a triangle has 2 sides with lengths 4 and 6, what is the range of the 3rd side?
6. Given the following triangle, what is the possible range of x?
7.
The smallest side is opposite of the ____________________________
The largest angle is opposite of the _____________________________
8. Given a triangle with the following side lengths: =
AB 3,=
AC 5,=
BC 4 . Draw the triangle and then
order the angles from smallest to largest.
9. Given a triangle with the following angle measures: m∠
=
A 50o , m∠=
B 100o , m∠=
C 30o . Draw the
triangle and then order the side lengths from largest to smallest.
Applying Congruence (4.2)
10. Two figures are congruent if they have the same ___________________ and _______________________.
11. What is a congruence statement? State 6 pieces of information you can get from the statement.
12. In the diagram, ∆EFG ≅ ∆OPQ. Complete the statement.
13 cm
a)
b)
c)
d)
e)
f)
g)
EF ≅ _____
∠P ≅ _____
∠G ≅ _____
m∠O = _____
QO = _____
∆GFE ≅ _____
x = _____
110o
7 cm
(3x-10)o
50o
13. What is the Third Angles Theorem?
14. Given Given ∆ ABC ≅ ∆DEF . Find the values of the variables.
x = _________
y = _________
15. Label the two triangles with the given information and solve for x, y, and z. Show all work.
Given : ∆APT≅ ∆WOC.
m∠A = 30°
x = ______
m∠P = 100°
m∠W = (y + 20)°
y = ______
m∠O = (x – 20)°
z = ______
m∠C = (z +30)°
Proving Triangles are Congruent (4.3-4.5)
16. Name the 5 Congruence Theorems/Postulates we learned to prove 2 triangles are congruent.
17. State the Theorem/Postulate that proves the two triangles are congruent. State NEI for “not enough
information”.
__________
__________
__________
__________
__________
__________
18. Why doesn’t SSA work? Give a counterexample.
19. Why doesn’t AAA work? Give a counterexample.
State the third congruence that must be given to prove that ∆JRM ≅ ∆DFB using the indicated postulate or
theorem.
20. GIVEN: JR ≅ DF , RM ≅ FB
____ ≅ ____ Use the SSS Congruence Postulate.
21. GIVEN: JR ≅ DF , RM ≅ FB
____ ≅ ____ Use the SAS Congruence Postulate.
22. GIVEN: JM ≅ DB J is a right angle and ∠J ≅ ∠D ____ ≅ ____Use the HL Theorem.
23. GIVEN: R ≅ F , RM ≅ FB
24. GIVEN: R ≅ F , RM ≅ FB
____ ≅ ____ Use the ASA Congruence Postulate.
____ ≅ ____ Use the AAS Congruence Theorem.
In the figures below mark any additional angles or sides that you know are congruent just from the given
information. Then state the postulate/theorem that proves the 2 triangles are congruent. State NEI for “not
enough information”.
25.
26.
27.
V
28.
P
S
29.
30.
H
For #31 – 33, decide if the following triangles are congruent. For each problem, do the following:
MARK YOUR FIGURES!
a) Can these triangles be proven congruent? Write “Yes” or “No”.
b) Name the congruent triangles (ONLY if they are congruent) and
c) State the postulate or theorem that supports your answer (ONLY if they are congruent)
31.
32.
33.
a) ___________________
a) ___________________
a) ___________________
b) ________ ≅ ________
b) ________ ≅ ________
b) ________ ≅ ________
c) ___________________
c) ___________________
c) ___________________
Mark your diagrams with the given information, and then mark any additional angles or sides that you know
are congruent. Then write out the proof.
34. Given: S is a midpoint of
Prove that
QU
QRS ≅ UTS


and
RT
Statements
S is a midpoint of
35. Given: DH
Prove that
QU
and
Reasons
RT
⊥ GE , F is a midpoint of GE , and DE ≅ GH
DEF ≅ HGF


Statements
DH ⊥ GE , F is a midpoint of GE , and DE ≅ GH
Reasons
CPCTC (4.6)
36. What does CPCTC stand for? When do we use it?
AB  DC and AD  BC
Prove that AD ≅ BC
37. Given:
Statements
AB  DC
and
38. Given:
BD bi sec ts ∠ABC
Reasons
AD  BC
BD ⊥ AC
Prove:
AB ≅ BC
Statements
Reasons

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