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Q8.

Expert-verified
Found in: Page 378

### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279

# Draw any obtuse $\Delta OBT$. Use the $SSS$ method to construct a triangle congruent to $\Delta OBT$.

By $SSS$ congruency $\Delta OBT\cong \Delta PQR$.

See the step by step solution

## Step 1. Given information.

An obtuse $\Delta OBT$ is given.

## Step 2. Draw the obtuse triangle.

Obtuse $\Delta OBT$ is drawn below.

Here, $\Delta OBT$ is an obtuse triangle as $\angle OBT>90°$.

## Step 3. Concept used.

According to $SSS$ 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 $\Delta PQR$ such that $PQ\cong OB, PR\cong OT, QR\cong BT$.

So,

$\Delta OBT\cong \Delta PQR$ (by $SSS$ congruence criteria)

Therefore, by $SSS$ congruency $\Delta OBT\cong \Delta PQR$.