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In triangle ABC, AB = AC. Points D and E lie on BC such that BD = CE. Perpendiculars DP and EQ are drawn to AB and AC respectively, and it is found DP = EQ.
Using the right triangles BDP and CEQ (right angles at P and Q), which rule and which equal parts justify their congruence?

Class 9SSS and RHS CongruenceGeometry — Triangles
  • ARHS, using equal hypotenuses BD = CE and equal legs DP = EQ
  • BSSS, using three equal sides
  • CAAA, using three equal angles
  • DSSA, using two sides and an angle

Step-by-Step Solution

Triangles BDP and CEQ are right-angled at P and Q. Hypotenuses BD = CE (given) and legs DP = EQ (given), so by RHS the triangles are congruent.
Answer: A) RHS, using equal hypotenuses BD = CE and equal legs DP = EQ

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