Chapter 11.2, Problem 13PPS

To determine

To find: Whether the given two triangles are congruent or not.

Answer to Problem 13PPS

The two given triangles are not congruent.

Explanation of Solution

Given information:

The two triangles given $\Delta MNO\text{ and }\Delta PQR$ are such that in $\Delta MN0,<M={78}^0,<N={65}^0,<O={37}^0,MN=8m,NO=13m,OM=12m$ and $\Delta PQR,<P={42}^0,<Q={63}^0,<R={75}^0,PQ=13m,QR=9m,RP=12m$ .

Concept and Formula Used:

The concept of congruent triangles is used. Two triangles are said to be congruent if their corresponding sides and the corresponding angles are equal.

Calculation:

The two triangles given $\Delta MNO\text{ and }\Delta PQR$ are such that in $\Delta MN0,<M={78}^0,<N={65}^0,<O={37}^0,MN=8m,NO=13m,OM=12m$ and $\Delta PQR,<P={42}^0,<Q={63}^0,<R={75}^0,PQ=13m,QR=9m,RP=12m$ .

And clearly as we see none of the angles in the two triangles are equal to each other, therefore, the two triangles are not congruent.

Conclusion:

The two given triangles are not congruent.