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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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Prove by the indirect method:
Given: Scalene Δ X Y Z in which Z W ¯ bisects X Z Y
(point W lies on X Y ¯ ).
Prove: Z W ¯ is not perpendicular to X Y ¯

To determine

To prove:

The line ZW¯ is not perpendicular to the side XY¯.

Explanation

Definition:

A triangle with three sides have different length is called scalene triangle.

Given:

The scalene triangle ΔXYZ in which ZW¯ bisects XZY and point W lies on XY¯.

Calculation:

Consider the triangle ΔXYZ,

Figure (1)

Assume, the line ZW¯ is perpendicular to the side XY¯.

Consider the triangles,

ΔXWZ and ΔYWZ

Since, the line ZW¯ is perpendicular to the side XY¯ then, the angles XWZ and YWZ is right angles. So,

XWZYWZ

Since, the line ZW¯ bisects the angle XZY into two congruent angles

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