# Lesson 7

Angle-Side-Angle Triangle Congruence

- Let’s see if we can prove other sets of measurements that guarantee triangles are congruent, and apply those theorems.

### 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 \(ABD\).

### Problem 5

Which conjecture is possible to prove?

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

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

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

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

### 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?

### 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 \(CA\)?

\(BA\)

\(BD\)

\(CB\)

\(AD\)