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Q8.

Expert-verified

Geometry

Found in: Page 378

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

Draw any obtuse $Δ O B T$ . Use the $S S S$ method to construct a triangle congruent to $Δ O B T$ .

By $S S S$ congruency $Δ O B T ≅ Δ P Q R$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

An obtuse $Δ O B T$ is given.

Step 2. Draw the obtuse triangle.

Obtuse $Δ O B T$ is drawn below.

Here, $Δ O B T$ is an obtuse triangle as $∠ O B T > 90 °$ .

Step 3. Concept used.

According to $S S S$ congruence criteria,

if all the sides of one triangle are congruent to the corresponding sides of other triangle,

then the two triangles are said to be congruent.

Step 4. Construct the congruent triangle.

Construct $Δ P Q R$ such that $P Q ≅ O B, P R ≅ O T, Q R ≅ B T$ .

So,

$Δ O B T ≅ Δ P Q R$ (by $S S S$ congruence criteria)

Therefore, by $S S S$ congruency $Δ O B T ≅ Δ P Q R$ .

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