Q16 Given: ABCX聽is a is a localid="... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 5: Q16 (page 169)

Given: $ABCX$ is a is a localid="1637648903053" $鈻�, DXFE$ is a $鈻�$ .
Prove: $鈭� B 鈮� 鈭� E$

Short Answer

Expert verified

It is proved that $鈭� B 鈮� 鈭� E$ .

Step by step solution

Step 1. Property of parallelogram.

The opposite angles of a parallelogram are congruent.

It is given that ABCX is a parallelogram in which $鈭� B$ and $鈭� A X C$ are opposite angles of a parallelogram. Then by property of parallelogram, $鈭� B 鈮� 鈭� A X C$ .

Step 2. Vertical opposite angles.

From the figure, it can be observed that $鈭� A X C$ and $鈭� D X F$ are vertically opposite angles. Therefore, by the definition of vertically opposite angles, $鈭� A X C 鈮� 鈭� D X F$ .

Step 3. Property of parallelogram.

It is given that DEFX is a parallelogram in which $鈭� E$ and $鈭� D X F$ are opposite angles of a parallelogram. Then by property of parallelogram, $鈭� D X F 鈮� 鈭� E$ .