# Angle-Side-Angle Triangle Congruence

ID: salur-zatuk Illustrative Math
Subject: Geometry

# Angle-Side-Angle Triangle Congruence

Classroom:
Due:
Student Name:
Date Submitted:
##### 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) $\text{All triangles with at least one side length of 5 are congruent.}$b) $\text{All pentagons with at least one side length of 5 are congruent.}$c) $\text{All rectangles with at least one side length of 5 are congruent.}$d) $\text{All squares with at least one side length of 5 are congruent.}$
##### 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) $AD$