Question

In triangleABC and trianglePQR,AB=PQ and AC=PR and altitude AM and altitude PN are equal. Show that triangleABC congruent to trianglePQR.

Answer 1

Solution:-
In Δ ABM and Δ PQN,
∠ AMB = ∠ PNQ = 90° (Since altitudes are perpendicular)
AB = PQ  (Given)
AM = PN  (Given)
By RHS congruency ;
Δ ABM is equal to Δ PQN,
Similarly, Δ ACM is congruent to Δ PRN
Therefore, ABM + ACM is congruent to PQN + PRN
Hence Δ ABC is congruent to Δ PQR