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Q26.

Expert-verified

Geometry

Found in: Page 127

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

Copy each three-dimensional figure and with coloured pencils outline the triangles listed. What postulate proves that these triangles are congruent?
Given: Cube whose faces are congruent squares.
Show: $△ ABF$ , $△ BCG$

The diagram outlining the triangles listed is:

The postulate that proves the given triangles are congruent is SAS postulate.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1 - Draw the labelled diagram outlining the triangles △ABF and △BCG.

The diagram outlining the triangles $△ A B F$ and $△ B C G$ is:

Step 2 - Description of step.

As, cube is having faces which congruent squares.

Therefore, $A B = B C = B F = C G$ and $∠ A B F = ∠ B C G = 90 °$

That implies, $A B ≅ B C ≅ B F ≅ C G$ and $∠ A B F ≅ ∠ B C G$ .

Step 3 - Description of step.

In the triangles $△ A B F$ and $△ B C G$ , it can be seen that $A B = B C$ , $∠ A B F = ∠ B C G = 90 °$ and $B F = C G$ .

Therefore, the triangles $△ A B F$ and $△ B C G$ are the congruent triangles by using the SAS postulate.

Step 4 - Write the conclusion.

The postulate that proves the given triangles are congruent is SAS postulate.

Most popular questions for Math Textbooks

In the following figure, the two-triangle shown are congruent. Then complete the following statement.

$B O =___$

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

For the following figure, do the SAS postulates justify that the two triangles are congruent?

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

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

For the following figure, does the SAS postulates justify that the two triangles are congruent.

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