**Topic: Geometric Proof - Similar Triangles****Problem Statement:**2. In $ \triangle ABC $, $BC \perp AC $ and $ DE \perp AB $. Prove $ \triangle ABC \sim \triangle ADE $.The diagram accompanying the problem depicts two triangles, $ \triangle ABC $ and $ \triangle ADE $, sharing a common vertex $ A $. The vertices are labeled as follows: $ A $ is the top vertex, $ B $ is the bottom left vertex, $ C $ is the bottom right vertex, $ D $ is a midpoint on segment $ AC $, and $ E $ is a point on segment $ AB $.**Proof Layout:***(Column 1: Statements, Column 2: Reasons)*| **Statement** | **Reason** ||-----------------------------------------|--------------------------|| 1. $ BC \perp AC $ and $ DE \perp AB $ | 1. GIVEN |### Diagram Explanation:- The diagram features two right-angled triangles, $ \triangle ABC $ and $ \triangle ADE $.- In $ \triangle ABC $, $ BC $ is perpendicular to $ AC $, confirming that $ \angle BCA $ is a right angle.- Similarly, in $ \triangle ADE $, $ DE $ is perpendicular to $ AB $, confirming that $ \angle DEA $ is a right angle.- The goal is to prove the similarity of these two triangles: $ \triangle ABC \sim \triangle ADE $.

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Answered: 2. In A ABC, BCAC and DE1 AB. Prove A…

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2. In A ABC, BCAC and DE1 AB. Prove A ABC~A ADE Statement Reason 1. BC LACand DE 1 AB 1. GIVEN

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

**Topic: Geometric Proof - Similar Triangles**

**Problem Statement:**
2. In $ \triangle ABC $, $BC \perp AC $ and $ DE \perp AB $. Prove $ \triangle ABC \sim \triangle ADE $.

The diagram accompanying the problem depicts two triangles, $ \triangle ABC $ and $ \triangle ADE $, sharing a common vertex $ A $. The vertices are labeled as follows: $ A $ is the top vertex, $ B $ is the bottom left vertex, $ C $ is the bottom right vertex, $ D $ is a midpoint on segment $ AC $, and $ E $ is a point on segment $ AB $.

**Proof Layout:**

*(Column 1: Statements, Column 2: Reasons)*

| **Statement** | **Reason** |
|-----------------------------------------|--------------------------|
| 1. $ BC \perp AC $ and $ DE \perp AB $ | 1. GIVEN |

### Diagram Explanation:
- The diagram features two right-angled triangles, $ \triangle ABC $ and $ \triangle ADE $.
- In $ \triangle ABC $, $ BC $ is perpendicular to $ AC $, confirming that $ \angle BCA $ is a right angle.
- Similarly, in $ \triangle ADE $, $ DE $ is perpendicular to $ AB $, confirming that $ \angle DEA $ is a right angle.
- The goal is to prove the similarity of these two triangles: $ \triangle ABC \sim \triangle ADE $.

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