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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

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
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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**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: \( \triangle ABC \sim \triangle ADE \).
Transcribed Image Text:**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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