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Core Connections Integrated II, 2015

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Core Connections Integrated II, 2015 View details

2. Section 8.2

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Exercise 29 Page 441

Consider the AAS (Angle-Angle-Side) Congruence Theorem.

See solution.

Practice makes perfect

We will start by proving that AB ≅ ED. Let's add the given information, BC≅ DC and ∠ A≅ ∠ E, to the diagram.

Examining the diagram, we also see a vertical angle pair at C. According to the Vertical Angles Theorem, these are congruent.

Now we can claim that △ ABC≅ △ EDC by the AAS (Angle-Angle-Side) Congruence Theorem. Since AB and ED are corresponding sides, they must be congruent.

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

Statement	Reason
1. BC= DC, ∠ A ≅ ∠ E	1. Given
2. ∠ BCA≅ ∠ DCE	2. Vertical Angles Theorem
3. △ ABC ≅ △ EDC	3. AAS Congruence Theorem
4. AB≅ ED	4. ≅ Δ → ≅ parts

Subchapter links

8.2.1 Angles of Polygons p.440-441

8.2.2 Areas of Regular Polygons p.445-448