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Q33

Expert-verified

Geometry

Found in: Page 171

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

Find something interesting to prove. Then prove it. Answers may vary.
Given: $▱ ABCD; ∠ 1 ≅ ∠ 2$

It is proved that $\bar{A X} ≅ \bar{C Y}$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Apply property of parallelogram.

The opposite sides of a parallelogram are congruent.

In $▱ A B C D$ , $\bar{A D}$ and $\bar{B C}$ are opposite sides. Therefore, $\bar{A D} ≅ \bar{B C}$ .

Step 2. Description of step.

From the given figure, it can be observed that $\bar{A D} ∥ \bar{B C}$ and $\bar{A C}$ is a transversal then $∠ D A C$ and $∠ A C B$ are alternate interior angles such that, $∠ D A C ≅ ∠ A C B$ .

Step 3. Description of step.

As $∠ 1 ≅ ∠ 2$ , $\bar{A D} ≅ \bar{B C}$ and $∠ D A C ≅ ∠ A C B$ then by ASA postulate, $Δ D A X ≅ Δ B C Y$ .

Step 4. Description of step.

As $Δ D A X ≅ Δ B C Y$ , then by corresponding parts of congruent triangles, $\bar{A X} ≅ \bar{C Y}$ .

Hence it is proved that $\bar{A X} ≅ \bar{C Y}$ .

Most popular questions for Math Textbooks

For exercises, 14-18 write paragraph proofs.

Given: parallelogram ABCD; W, X, Y, Z are midpoints of $\bar{AO}$ , $\bar{BO}$ , $\bar{CO}$ and $\bar{DO}$ .

Prove: role="math" localid="1637745814874" $WXYZ$ is a parallelogram.

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Prove: localid="1637661691185" $\bar{A B} ≅ \bar{C E}$

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