Question

In the given figure, PA is perpendicular to AB, QB is perpendicular to AB and PA = QB. Prove that triangle OAP is congruent to triangle OBQ. Is OA = OB​

Answer 1

Answer:

Step-by-step explanation:

In Δ OAP & Δ  OBC ,

PA = QB (given)

∠ AOP = ∠ BOC (Vertically Opp Angles)

∠ A = ∠ B (each 90°)

By AAS ≅ Criterion

Δ OAP ≅Δ OBC

∴ OA = OB (c.p.c.t)

Answer 2

Answer:

Given

PA is perpendicular to AB

QB is perpendicular to AB

PA =QB

R.T.P : TRIANGLE OAP IS CONGRUENT TO TRIANGLE OBQ

BY ASA CONGRUENCE RULE

ΔOAP      ΔOBQ

∠PAO            ∠QBO  (A)     Given

  PA                   QB    (S)    Given

∠POA             ∠BQO (A)    Vertically opposite angles are equal

By ASA congruence rule

ΔOAP ≅ ΔOBQ

By CPCT (Congruent  parts of congruent  triangle)

OA=OB

Hence proved