Question

For the diagram above, both the triangles are

• A. Congruent by ASA or SSS congruency
• B. Congruent by Hypotenuse Leg or SSS congruency
• C. Not congruent

Answer 1

The correct option is B Congruent by Hypotenuse Leg or SSS congruency

Using the Pythagorean theorem on triangle $ABC$,
$A{C}^2=A{B}^2+B{C}^2\Rightarrow (25{)}^2=(24{)}^2+B{C}^2$
$\Rightarrow 625-576=B{C}^2$
We find $BC=7cm$
$\therefore$ For $\Delta PRQ$ and $\Delta ABC$:
$RQ=BC$ and $PQ=AC$
$\therefore$ By hypotenuse - leg congruency we found both triangles to be congruent.
Applying Pythagorean theorem in $\Delta PRQ,PR=24$ cm
Again for both the triangles we found:
$PR=AB;RQ=BC\&PQ=AC$
$\therefore$ By SSS congruency we conculde again that both the trianlges are congruent.