# Lesson 7

Angle-Side-Angle Triangle Congruence

### Problem 1

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

### Problem 2

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

• 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.
• Side $$DB$$ is congruent to side $$BD$$ because they're the same segment.
• Angle $$A$$ is congruent to angle $$C$$ because they're both right angles.
• By the Angle-Side-Angle Triangle Congruence Theorem, triangle $$BCD$$ is congruent to triangle $$DAB$$.

### Problem 3

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

### Problem 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 $$ABD$$.

### Solution

(From Unit 2, Lesson 6.)

### Problem 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.

### Solution

(From Unit 2, Lesson 5.)

### Problem 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?

### Solution

(From Unit 2, Lesson 4.)

### Problem 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:

$$AD$$