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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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In Exercise 27 to 29, prove the indicated relationship.

Chapter 3.2, Problem 28E, In Exercise 27 to 29, prove the indicated relationship. Given: DE bisects FDG FG Prove: E is

Given: D E bisects F D G
F G
Prove: E is midpoint of F G ¯

To determine

To prove:

The given statement.

Explanation

Given:

The following figure shows the given diagram.

Given that,

DE bisects FDG

FG

Approach:

By definition of ASA, if two angles and their included side of one triangle is congruent to two angles and their included side of second triangle, then triangle will be congruent.

The completed proof is shown in the following table.

PROOF
Statements Reasons
1. DE bisects FDG 1. Given
2. FDEGDE 2. If a ray divides an angle in to two .
s, then the ray bisects the right angle
3. FG 3. Given
4. DG¯FD¯ 4. Transitive property of triangle
5. ΔFDEΔEDG 5. ASA
6. FE¯EG¯ 6. CPCTC
7. E is midpoint of FG¯ 7

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