Angle-Side-Angle Triangle Congruence

ID: salur-zatuk
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Angle-Side-Angle Triangle Congruence

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Problem 1

1) What triangle congruence theorem could you use to prove triangle ADEADE is congruent to triangle CBECBE?

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Problem 2

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

1. Line ABAB is parallel to line DCDC and cut by transversal DBDB. So angles CDBCDB and ABDABD are alternate interior angles and must be congruent.

2. Side DBDB is congruent to side BDBD because they're the same segment.

3. Angle AA is congruent to angle CC because they're both right angles.

4. By the Angle-Side-Angle Triangle Congruence Theorem, triangle BCDBCD is congruent to triangle DABDAB.

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Problem 3

3) Segment GEGE is an angle bisector of both angle HEFHEF and angle FGHFGH. Prove triangle HGEHGE is congruent to triangle FGEFGE.

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Problem 4

4) Triangles ACDACD and BCDBCD are isosceles. Angle BACBAC has a measure of 33 degrees and angle BDCBDC has a measure of 35 degrees. Find the measure of angle ABDABD.

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Problem 5

5) Which conjecture is possible to prove?

a) All triangles with at least one side length of 5 are congruent.\text{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.\text{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.\text{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.\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 LKJLKJ. What is the least amount of additional information that Andre needs to construct a triangle congruent to this one?

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Problem 7

7) Here is a diagram of a straightedge and compass construction. CC is the center of one circle, and BB is the center of the other. Which segment has the same length as segment CACA?

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a) BA BA b) BD BD c) CB CB d) AD AD