# Angle-Side-Angle Triangle Congruence

# Angle-Side-Angle Triangle Congruence

##### 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?

##### 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 $CA$?