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Elementary Geometry for College St...

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

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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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In Exercise 17 to 20, first prove that triangles are congruent then use CPCTC.

Given: D E ¯ E F ¯ and C B ¯ A B ¯
A B ¯ F E ¯
A C ¯ F D ¯
Chapter 3.2, Problem 20E, In Exercise 17 to 20, first prove that triangles are congruent then use CPCTC. Given: DEEF and CBAB
Prove: E F ¯ B A ¯

To determine

To prove:

The given statement.

Explanation

Given:

The following figure shows the given diagram.

Given that,

DE¯EF¯ and CB¯AB¯

AB¯FE¯

AC¯FD¯

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¯EF¯ and CB¯AB¯ 1. Given
2. BE 2. The angles formed by perpendicular lines are right angles and right angles are congruent..
3. AB¯FE¯ 3. Given
4. FA 4. If two parallel lines are cut by a transversal, then the alternate interior angles will be congruent.
5. AC¯FD¯ 5. Given
7

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