Free Printable Congruent Triangle Proofs Review

1.

Given triangle ABC is congruent to triangle MNO, identify all pairs of congruent corresponding parts.

a)

∠A ≅ ∠M, ∠B ≅ ∠N, ∠C ≅ ∠O, AB ≅ MN, BC ≅ NO, AC ≅ MO

b)

∠A ≅ ∠M, ∠B ≅ ∠O, ∠C ≅ ∠N, AB ≅ MN, BC ≅ NO, AC ≅ MO

c)

∠A ≅ ∠M, ∠B ≅ ∠N, ∠C ≅ ∠O, AB ≅ MO, BC ≅ NO, AC ≅ MN

d)

∠A ≅ ∠O, ∠B ≅ ∠N, ∠C ≅ ∠M, AB ≅ NO, BC ≅ MN, AC ≅ MO

2.

Given that triangle ABC is congruent to triangle DEC and the measure of angle E is 23 degrees, find the measure of angle ACB.

a)

23°

b)

67°

c)

113°

d)

157°

3.

What additional information do you need to prove that triangle ABC is congruent to triangle ADC by the SAS Postulate?

a)

AB ≅ AD

b)

∠ACB ≅ ∠ACD

c)

∠ABC ≅ ∠ADC

d)

BC ≅ DC

4.

ΔHLK is isosceles with base HK, ∠IHL and ∠JKL are right angles, IK ≅ JH. Refer to the figure, which of the following statements is true?

a)

ΔHIL ≅ ΔKJL by HL

b)

ΔHLK ≅ ΔJLK by SSS

c)

ΔHKI ≅ ΔHJK by SAS

d)

There are no congruent triangles.

5.

Refer to the figure shown, which of the following statements is true?

a)

ΔTUV ≅ ΔXWV by ASA

b)

ΔTUV ≅ ΔVWX by SAS

c)

ΔTUV ≅ ΔWXV by SAS

d)

ΔTUV ≅ ΔWXV by SSS

6.

Given: ∠B ≅ ∠E and ∠C ≅ ∠F. What other piece of information is needed to show ΔABC ≅ ΔDEF by ASA Congruence Postulate?

a)

EF ≅ FE

b)

BC ≅ EF

c)

∠A ≅ ∠D

d)

∠B ≅ ∠F

7.

Which postulate or theorem would you use to tell whether ΔABC ≅ ΔDEF with the given information?

∠C ≅ ∠F, AC ≅ DF, and BC ≅ EF

a)

SSS

b)

SAS

c)

ASA

d)

AAS

8.

Which postulate or theorem would you use to tell whether ΔABC ≅ ΔDEF with the given information?

AB ≅ DE, ∠C ≅ ∠F, and ∠B ≅ ∠E

a)

SSS

b)

SAS

c)

ASA

d)

AAS

9.

Which postulate or theorem would you use to tell whether ΔABC ≅ ΔDEF with the given information?

AC ≅ DF, ∠C ≅ ∠F, and ∠A ≅ ∠D

a)

SSS

b)

SAS

c)

ASA

d)

AAS

10.

What is Reason D?

a)

SSS Congruence

b)

SAS Congruence

c)

ASA Congruence

d)

AAS Congruence

e)

HL Congruence

11.

The fronts of the houses are identical. What is the length of side LM?

a)

12 ft

b)

20 ft

c)

32 ft

12.

Congruent by

a)

SSS

b)

SAS

c)

ASA

d)

AAS

13.

What additional information is needed to prove the two triangles are congruent by SAS?

a)

$\angle Q\ \cong\ \angle T$

b)

$\overline{QS}\ \cong\overline{TU}$

c)

$\overline{PR}\ \cong\ \overline{SU}$

d)

$\angle R\ \cong\ \angle\ U$

14.

What additional information is needed to prove the two triangles are congruent by ASA?

a)

$\overline{KN}\ \cong\overline{QM}$

b)

$\angle N\ \cong\angle M$

c)

$\overline{LN}\ \cong\ \overline{PM}$

d)

$\angle L\ \cong\ \angle P$

15.

What is the "statement" for step 3 of the proof?

a)

∡EDA≅∡DCB

b)

∡AED≅∡BEC

c)

DE=CE

d)

∡AED≅∡CED

16.

Use the picture to answer the question.

a)

76

b)

28

c)

152

d)

56

17.

What is #4 Statement?

a)

∠MNL ≌ ∠ONP

b)

MN ≌ ON

c)

N ≌ N

d)

MO ≌ OM

18.

What is #2 Reason?

a)

Same Line

b)

Reflexive Property

c)

Segment Bisector

d)

Definition of Midpoint

19.

What is #3 Reason?

a)

Alternate Exterior Angles are congruent when formed by parallel lines

b)

Alternate Interior Angles are congruent when formed by parallel lines

c)

Vertical Angles are congruent

d)

Definition of Angle Bisector

20.

What is #4 Reason?

a)

Alternate Interior Angles are congruent when formed by parallel lines

b)

Vertical Angles are congruent

c)

Reflexive Property

d)

Definition of Angle Bisector

21.

What is #4 Statement?

a)

All of correct

b)

SP ≌ SP

c)

PS ≌ SP

d)

PS ≌ PS

22.

Which of the following is a correct statement and reason for the proof shown?

a)

$\angle APB\cong\angle CPD$ ; Vertical angles are congruent

b)

$\angle A\approx\angle D$ ; Alternate Interior angles are congruent when formed by parallel lines

c)

$\angle C\cong\angle B$ ; Alternate Interior angles are congruent when formed by parallel lines

d)

$\overline{AB}\cong\overline{CD}$ ; Prove

23.

Which of the following is a correct statement and reason for the proof shown?

a)

$\overline{DC}\cong\overline{DC}$ ; Reflexive Property

b)

$\angle A\cong\angle B$ ; Reflexive Property

c)

$\angle1\cong\angle2$ ; Reflexive Property

d)

$\overline{AD}\cong\overline{DB}$ ; Midpoint Theorem

24.

What is Reason C?

a)

SSS Congruence

b)

SAS Congruence

c)

ASA Congruence

d)

AAS Congruence

e)

HL Congruence

25.

What does CPCTC stand for?

a)

Corresponding Parts of Congruent Triangles are Congruent

b)

Congruent Parts of Congruent Triangles are Corresponding

c)

Colorful Pieces of Corresponding Triangles are Congruent

d)

Congruent Pieces of Congruent Triangles are Congruent

Congruent Triangle Proofs Review

Total questions: 25

Worksheet time: 1hrs 1mins

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