   Chapter 3.1, Problem 37E ### Elementary Geometry for College St...

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

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# In quadrilateral ABCD, A C ¯ and B D ¯ are perpendicular bisectors of each other. Name all triangles that are congruent to: a) Δ A B E b) Δ A B C c) Δ A B D To determine

a)

To find:

The name of the triangle is congruent to ΔABE.

Explanation

Procedure used:

The perpendicular bisectors, bisect each other equally and makes right angles.

Given:

The quadrilaterals ABCD is shown in the figure below,

Figure (1)

From figure (1),

AC¯ and BD¯ are perpendicular bisectors of each other.

Calculation:

Consider the triangles,

Since, AC¯ and BD¯ are perpendicular bisectors to each other. Then,

The side BE¯ and the side DE¯ are equal to each other. So,

BE¯DE¯

The side AE¯ and the side CE¯ are equal to each other. So,

AE¯CE¯

And, the angle AEB, the angle AED, the angle DEC and the angle BEC makes right angle, so

To determine

b)

The triangle ΔABC is congruent to the triangle.

To determine

c)

The triangle ΔABD is congruent to the triangle.

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