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Q2WE.

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Geometry

Found in: Page 124

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

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to $Δ A B C$ . If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

$Δ A B C ≅ Δ A D C$ by SAS postulates.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Check the figure.

Consider the figure.

Step 2. Apply the concept of ASA, SSS, SAS postulates.

The Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

The Side-Side-Side Postulate (SSS) says triangles are congruent if three sides of one triangle are congruent to the corresponding sides of the other triangle.

SAS Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent

Step 3. Step description.

From both the triangles $Δ A B C$ and $Δ A D C$ , it is clear that

role="math" localid="1648801461123" $\begin{array}{l} B C = C D \\ ∠ B C A = ∠ A C D \\ A C = A C \end{array}$

Therefore, the two triangles are congruent with the SAS postulate.

Thus, the triangles are congruent with the SAS postulate.

Most popular questions for Math Textbooks

The pentagons shown are congruent. Complete.

$BLACK ≅ \underline{?}$

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to $Δ A B C$ . If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

For the following figure, can the triangle be proved congruent? If so, what postulate can be used?

The pentagons shown are congruent. Complete.

$KB = \underline{?} cm$

$\bar{OR}$ is a common side of two congruent quadrilaterals.

Complete: quad. $NERO ≅$ quad $\underline{?}$ .

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