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Q29

Expert-verified

Geometry

Found in: Page 170

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

Given: $▱ PQRS;$ localid="1637659881844" $\bar{P J} ≅ \bar{R K}$
Prove: localid="1637659923835" $\bar{S J} ≅ \bar{Q K}$

It is proved that $\bar{S J} ≅ \bar{Q K}$ .

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.

From the given figure, it can be observed that $\bar{S P}$ and $\bar{R Q}$ are opposite sides of a $▱ P Q R S$ .

Therefore, $\bar{S P} ≅ \bar{R Q}$

Step 2. Apply property of parallelogram.

The opposite angles of a parallelogram are congruent.

From the given figure, it can be observed that $∠ P$ and $∠ R$ are opposite angles of a $▱ P Q R S$ .

Therefore, $∠ P ≅ ∠ R$ .

Step 3. Apply SAS postulate.

If two sides and the included angle of one triangle are congruent to two sides and included angle of another triangle, then the triangles are congruent.

Here, $\bar{P J} ≅ \bar{R K}$ , $∠ P ≅ ∠ R$ and $\bar{S P} ≅ \bar{R Q}$ , then by SAS postulate $Δ S P J ≅ Δ K R Q$ .

Step 4. Description of step.

As $Δ S P J ≅ Δ K R Q$ , then by corresponding parts of congruent triangles, $\bar{S J} ≅ \bar{Q K}$ .

Hence it is proved that $\bar{S J} ≅ \bar{Q K}$ .

Most popular questions for Math Textbooks

For the following figure, if $R E = E W$ then name all angles congruent to $∠ E R W$ .

Study the markings on each figure and decide whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies.

You can use a sheet of lined notebook paper to divide a segment into a number of congruent parts. Here a piece of cardboard with edge $\bar{AB}$ is placed so that $\bar{AB}$ is separated into five congruent parts. Explain why it works.

Given: ABCD is a $▱, ∠ A ≅ ∠ E$

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

What values must x and y have to make the quadrilateral a parallelogram?

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