Question

In $\Delta ABCand\Delta PQR,\angle A=\angle P,\angle R=\angle C,andAC=1.25\times PR.$.
Then, $\Delta ABCand\Delta PQR$ are:

• A. Similar as well as congruent
• B. Similar but not congruent
• C. Congruent but not similar
• D. Neither similar nor congruent

Answer 1

The correct option is B Similar but not congruent

In $\Delta ABCand\Delta PQR,$ since $\angle A=\angle P,\angle R=\angle C,\Delta ABCand\Delta PQR$ are similar triangles. [AA similarity criterion]

For two triangles to be congruent, they must have the same shape and the same size.$\Delta ABCand\Delta PQR$ have the same shape as their corresponding angles are equal. But, since $AC=1.25\times PR$, they do not have the same size. Hence, they are not congruent.

Thus,$\Delta ABCand\Delta PQR$ are similar but not congruent.