Question

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

Short answer

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

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 $\Delta OBT\cong \Delta PQR$.