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Found in: Page 207


Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279

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Short Answer

Write proofs in two-column form.

Given: VY¯YZ¯. Prove: VXZ is an obtuse angle.



1. Y+Z+YXZ=180

Angle sum property

2. YXZ+VXZ=180

Linear angles

See the step by step solution

Step by Step Solution

Step 1. Angles property of a triangle

The sum of the angles of a triangle is 180. If an angle is greater than 90 then it is an obtuse angle.

Step 2. Use the angle sum property and find the angle YXZ

Since VY¯YZ¯ therefore, XYZ=Y=90.

The sum of the angles of triangle will be:

role="math" localid="1637852883028" Y+Z+YXZ=180 Z+YXZ=180Y Z+YXZ=18090 Z+YXZ=90

Since Z>90, therefore YXZ<90.

Step 3. Prove the statement

From the figure

Use linear angle property as follows:


Since YXZ<90 therefore from equation (1) VXZ>90.

Therefore, VXZ is an obtuse angle.

Hence proved.

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