# Angle-Side-Angle Triangle Congruence

ID: zusuj-movab
Illustrative Mathematics, CC BY 4.0
Subject: Geometry

7 questions

# Angle-Side-Angle Triangle Congruence

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##### Problem 1

1) What triangle congruence theorem could you use to prove triangle ﻿$ADE$﻿ is congruent to triangle ﻿$CBE$﻿?

##### Problem 2

2) Han wrote a proof that triangle ﻿$BCD$﻿ is congruent to triangle ﻿$DAB$﻿. Han's proof is incomplete. How can Han fix his proof?

1. Line ﻿$AB$﻿ is parallel to line ﻿$DC$﻿ and cut by transversal ﻿$DB$﻿. So angles ﻿$CDB$﻿ and ﻿$ABD$﻿ are alternate interior angles and must be congruent.

2. Side ﻿$DB$﻿ is congruent to side ﻿$BD$﻿ because they're the same segment.

3. Angle ﻿$A$﻿ is congruent to angle ﻿$C$﻿ because they're both right angles.

4. By the Angle-Side-Angle Triangle Congruence Theorem, triangle ﻿$BCD$﻿ is congruent to triangle ﻿$DAB$﻿.

##### Problem 3

3) Segment ﻿$GE$﻿ is an angle bisector of both angle ﻿$HEF$﻿ and angle ﻿$FGH$﻿. Prove triangle ﻿$HGE$﻿ is congruent to triangle ﻿$FGE$﻿.

##### Problem 4

4) Triangles ﻿$ACD$﻿ and ﻿$BCD$﻿ are isosceles. Angle ﻿$BAC$﻿ has a measure of 33 degrees and angle ﻿$BDC$﻿ has a measure of 35 degrees. Find the measure of angle ﻿$ABD$﻿.

##### Problem 5

5) Which conjecture is possible to prove?

a)

All triangles with at least one side length of 5 are congruent.

b)

All pentagons with at least one side length of 5 are congruent.

c)

All rectangles with at least one side length of 5 are congruent.

d)

All squares with at least one side length of 5 are congruent.

##### Problem 6

6) Andre is drawing a triangle that is congruent to this one. He begins by constructing an angle congruent to angle ﻿$LKJ$﻿. What is the least amount of additional information that Andre needs to construct a triangle congruent to this one?

##### Problem 7

7) Here is a diagram of a straightedge and compass construction. ﻿$C$﻿ is the center of one circle, and ﻿$B$﻿ is the center of the other. Which segment has the same length as segment ﻿$CA$﻿?

a)

﻿$BA$﻿

b)

﻿$BD$﻿

c)

﻿$CB$﻿

d)

﻿$AD$﻿