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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 3.2, Problem 20E
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Elementary Geometry for College St...

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

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
23 views

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. ∠B≅∠E 2. The angles formed by perpendicular lines are right angles and right angles are congruent..
3. AB¯∥FE¯ 3. Given
4. ∠F≅∠A 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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Sect-3.1 P-1ESect-3.1 P-2ESect-3.1 P-3ESect-3.1 P-4ESect-3.1 P-5ESect-3.1 P-6ESect-3.1 P-7ESect-3.1 P-8ESect-3.1 P-9ESect-3.1 P-10E
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