Suggested languages for you:

Americas

Europe

Q10.

Expert-verified
Found in: Page 207

### Geometry

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

# Write proofs in two-column form.Given: $\overline{VY}\perp \overline{YZ}$. Prove: $\angle VXZ$ is an obtuse angle.

 Statement Reason 1. $\angle Y+\angle Z+\angle YXZ=180$ Angle sum property 2. $\angle YXZ+\angle VXZ=180$ Linear angles
See the 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 $\overline{VY}\perp \overline{YZ}$ therefore, $\angle XYZ=\angle Y=90$.

The sum of the angles of triangle will be:

role="math" localid="1637852883028" $\begin{array}{c}\angle Y+\angle Z+\angle YXZ=180\\ \angle Z+\angle YXZ=180-\angle Y\\ \angle Z+\angle YXZ=180-90\\ \angle Z+\angle YXZ=90\end{array}$

Since $\angle Z>90$, therefore $\angle YXZ<90$.

## Step 3. Prove the statement

From the figure

Use linear angle property as follows:

$\angle YXZ+\angle VXZ=180$

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

Therefore, $\angle VXZ$ is an obtuse angle.

Hence proved.