Chapter 12, Problem 13CUR

(a)

To determine

To write:The postulate or theorem that justifies the statement.

Answer to Problem 13CUR

The given statement is justified by all angle equal postulate.

Explanation of Solution

Given information: If $\angle J\cong \angle X$ and $\angle K\cong \angle Y$ , then $\Delta JKL\sim \Delta XYZ$ .

Calculation:

It is given that the two triangles $\Delta JKL\sim \Delta XYZ$ . So,

  $\begin{array}{l}\angle J\cong \angle X\\ \angle K\cong \angle Y\end{array}$

If two angles of triangles are congruent, then third angle will also be congruent.

  $\angle L\cong \angle Z$

Sum of all the angles are equal. So, both are similar to each other.

Therefore, $\Delta JKL\sim \Delta XYZ$ by the all angles equal postulate.

(b)

To determine

To find: The converse of the statement. Also, check that the converse is true or false.

Answer to Problem 13CUR

The converse statementis false.

Explanation of Solution

Given information:f $\angle J\cong \angle X$ and $\angle K\cong \angle Y$ , then $\Delta JKL\sim \Delta XYZ$ .

Calculation:

Given triangles are similar by all angle equal postulate.So, all angles are equal and may be corresponding sides are in equal ratio.

Converse statement is not true always.

Therefore, the converse statement is false.