Q38 Prove: If a segment whose endpoi... [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: Q38 (page 171)

Prove: If a segment whose endpoints lie on opposite sides of a parallelogram passes though the midpoint of a diagonal, that segment is bisected by the diagonal.

Short Answer

Expert verified

It is proved that segment is bisected by diagonal.

Step by step solution

Step 1. Draw a diagram with appropriate instruction.

Consider a parallelogram ABCD. $\overset{炉}{B D}$ is a diagonal of that parallelogram. $\overset{炉}{E F}$ is the line segment that bisects the diagonal.

Step 2. Description of step.

As ABCD is a parallelogram and opposite sides of a parallelogram are equal. $\overset{炉}{B D}$ is a transversal. Then alternate interior angles are congruent $鈭� F D G 鈮� E B G$ .

As $\overset{炉}{E F}$ is the line segment which bisects the diagonal then, $\overset{炉}{D G} = \overset{炉}{G B}$ .

Step 3. Description of step.

Consider $螖 D G F$ and $螖 B G E$ , $鈭� D G F 鈮� 鈭� B G E$ , $\overset{炉}{D G} = \overset{炉}{G B}$ and $鈭� F D G 鈮� E B G$ then by ASA postulate $螖 D G F 鈮� 螖 B G E$ .