Chapter 12, Problem 39CR

To determine

To check: Whether the area of the other triangle can be found or not if two sides on one triangle are equal to two sides of another triangle.

Answer to Problem 39CR

Area of the second triangle cannot be found.

Explanation of Solution

Given Information:

Two sides of one triangle are equal to the two sides of another triangle.

The included angles of two triangles are supplementary.

Formula used:

Sum of supplementary angles $={180}^{\text{o}}$

Calculation:

Let $ABC\text{}\text{and}PQR$ be two triangles

We have $AB=PQ\text{and}BC=QR$

  $\angle B+\angle Q={180}^{\text{o}}$

From these data, we cannot conclude that one of the angles of one triangle is equal to one of the angles of another triangle.

To apply similarity or congruency, we need at least one pair of angles equal.

So, we cannot apply either similarity or congruency in these two triangles.

Hence, area of the second triangle cannot be found.