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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 2 Page 628

∠ ACB and ∠ DCE are vertical angles.

See solution.

Practice makes perfect

From the diagram, we know that an angle and a side are congruent in △ ABC and △ DEC. Observing the diagram, we can also identify two vertical angles, ∠ ACB and ∠ DCE. 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. &AB ⊥ AD, DE ⊥ AD &AC ≅ DC	1. Given
2. ∠ BAC and ∠ EDC are right angles	2. Definition of perpendicular lines
3. ∠ BAC≅ ∠ EDC	3. Right Angles Congruence Theorem
4. ∠ ACB and ∠ DCE are vertical angles	4. Definition of vertical angles as shown in the diagram
5. ∠ ACB ≅ ∠ DCE	5. Vertical Angles Congruence Theorem
6. △ ABC ≅ △ DEC	6. ASA Congruence Theorem

Subchapter links

Communicate Your Answer p.625

Monitoring Progress p.627-629

Exercises p.630-632

Exercise 2 Page 628

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Alternative Solution