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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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Given: In rt Δ A B C , A D ¯ bisects C A B and B F ¯
bisects A B C .
Find: m F E D

Chapter 2.4, Problem 50E, Given: In rt ABC, AD bisects CAB and BF bisects ABC. Find: mFED

To determine

The measure of angle mFED.

Explanation

Given:

In right ΔABC, AD¯ bisects CAB and BF¯ bisects ABC.

Definition:

Angle bisector bisects the angle in half.

The sum of the measures of interior angles of a triangle is 180°.

If two lines intersect each other than the vertical angle formed are congruent to each other and their measures are same.

Calculation:

Consider the given figure.

Figure (1)

Consider the right triangle ΔABC,

mABC+mCAB+mC=180°(1)

Substitute 90° for mC in the equation (1).

mABC+mCAB+90°=180°mABC+mCAB=180°90°mABC+mCAB=90°(2)

Since, the angle bisector bisects the angle in half, then from the figure (1)

mBAE=12(

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