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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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G i v e n : D B ¯ A C ¯ A D ¯ D C ¯ m C = 70 ° F i n d : m A D B Chapter 3.CR, Problem 21CR, Given:DBACADDCmC=70Find:mADB

To determine

The value of mADB.

Explanation

Procedure used:

If two sides of the triangle are equal then the corresponding angles are also equal in the triangle.

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

Given:

The triangle ΔACD is shown in the figure below,

Figure (1)

From figure (1),

DB¯AC¯AD¯DC¯mC=70°

Calculation:

Consider the triangle ΔACD,

From the given data,

The segment DB¯ is perpendicular to the side AC¯, then the angle formed by the perpendicular is equal to right angle. So,

mABD=90°

Since, the side AD¯ is congruent to the side DC¯, then the congruent side have same measures. So,

AD¯=DC¯

Since, the two sides of the triangle are equal then the corresponding angles are also equal in the triangle

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