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Big Ideas Math Integrated I, 2016 View details

6. Proving Triangle Congruence by ASA and AAS

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Exercise 3 Page 629

∠ RTS and ∠ UTV are vertical angles.

See solution.

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From the diagram, we know that an angle and a side are congruent in △ RST and △ TUV. Observing the diagram, we can also identify two vertical angles, ∠ RTS and ∠ UTV. By the Vertical Angles Congruence Theorem, these angles are congruent as well.

Now we have enough information to prove congruence using the ASA Congruence Theorem.

Alternative Solution

Two-Column Proof

Let's show this as a two-column proof as well.

Statement	Reason
1. ∠ S ≅ ∠ U, RS ≅ VU	1. Given
2. ∠ RTS and ∠ UTV are vertical angles	2. Definition of vertical angles as shown in the diagram
3. ∠ RTS ≅ ∠ UTV	3. Vertical Angles Congruence Theorem
4. △ RST ≅ △ VUT	4. AAS Congruence Theorem

Subchapter links

Communicate Your Answer p.625

Monitoring Progress p.627-629

Exercises p.630-632

Exercise 3 Page 629

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Alternative Solution