# 4.3- Proving Triangles Congruent

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Chapter 4- Lesson 3                                                                                      Write congruent state-
ments for congruent tri-
Proving Triangles Congruent                                                                              angles.

Prove triangles are con-
In the previous lesson you constructed triangles when given vari-                                        gruent using SSS, ASA,
ous sides and angles. Sometimes this resulted in a unique trian-                                         SAA, and SAS.
gle. In this lesson you will use those ideas to determine, and to
prove, if two triangles are congruent.

1. Do you really need to know that ALL three pairs of angles and ALL three pairs of
sides are congruent before you can conclude that the triangles are congruent? What
is the least information you could have and still be justiﬁed to conclude that the tri-
angles must be congruent? Explain.

2. What are the three triangle congruence postulates? Write them in “If ___, then___”
form.

3. Consider the pair of triangles shown below. Are they congruent?

F
A B = 6.14 cm     B                                     76.0°         F E = 6.46 cm
B C = 7.76 cm                        D                                D F = 6.14 cm
C A = 6.46 cm                              53.8°                      D E = 7.76 cm
53.8°

50.2°

76.0°
50.2°
E
A                             C

Draw arrows to show how the angles from the triangle on the left correspond (match
up) to the angles from the triangle on the right.

Write a congruence statement for the triangles above.

Critical and Informed Thinkers • Effective Communicators • Collaborative Workers
Chapter 4: Lesson 3- Proving Triangles Congruent

4. Consider the pairs of triangles below. If possible, complete the congruence state-
ment and state the appropriate congruence postulate. Otherwise, explain why you
can not conclude that the triangles must be congruent.

a)                                    b)
c)
E
A                   B
Q                    R

G
D                    C           F                            H                  P                    O

ABD ≅__ __ __                          FGE ≅__ __ __                          QPR ≅__ __ __

d)                                                e)
f)
K                                              U
A                       D
M
L                                                            W

V
J                                                T
B                        C
N                                           S

LMN ≅__ __ __                                   UTV ≅__ __ __                      __ __ __ ≅ABD

5. Using separate paper, write a proof for each of the ﬁgures above for which a true
congruence statement could be written. Include a sketch, a given statement and a
prove statement for each of the proofs.

Responsible Members of Society • Critical and Informed Thinkers • Effective Communicators • Collaborative Workers • Self Directed Learners

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