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Big Ideas Math Integrated I, 2016 View details

7. Using Congruent Triangles

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Exercise 10 Page 637

Notice that ∠ 1 and ∠ 2 are exterior angles.

See solution.

Practice makes perfect

How should we prove congruence?

We notice that ∠ 1 and ∠ 2 are exterior angles to △ AEB and △ DEC, respectively. Therefore, we should likely use the Exterior Angle Theorem to prove that ∠ 1 ≅ ∠ 2.

Plan for proving congruence

Our plan includes 2 steps.

Show that ∠ 1 and ∠ 2 are exterior angles to the non-adjacent angles of △ AEB and △ DEC respectively.
Show that m∠ 1 = m∠ 2 by the Transitive Property of Equality.

Proof

Two-Column Proof

Finally, we can prove ∠ 1 ≅ ∠ 2 using a two-column proof.

Statement	Reason
1. &∠ AEB ≅ ∠ DEC &∠ BAE ≅ ∠ CDE	1. Given
2. &m∠ AEB = m∠ DEC &m∠ BAE = m∠ CDE	2. Definition of congruent angles
3. &m∠ AEB+m∠ BAE=m∠ 1 &m∠ DEC+m∠ CDE=m∠ 2	3. Exterior Angle Theorem
4. &m∠ AEB+m∠ BAE=m∠ 1 &m∠ AEB+m∠ BAE=m∠ 2	4. Substitution Property of Equality
5. m∠ 1=m∠ 2	5. Transitive Property of Equality
6. ∠ 1≅ ∠ 2	6. Definition of congruent angles

Subchapter links

Communicate Your Answer p.633

Monitoring Progress p.634-635

Exercise 10 Page 637

Hints

Check the answer

Practice exercises

Assess your skill

How should we prove congruence?

Plan for proving congruence

Proof