Question

Given: Quadrilateral PQRS is a rectangle. Prove: PR = QS

Answer 1

Answer:

Given: Quadrilateral P QR S  is a rectangle.

To prove :PR= Q S

Construction : Join PR and Q S.

Proof: In Rectangle PQRS, and

→ taking two triangles PSR and Δ QRS

  1. PS = Q R

  2.  ∠ PS R  = ∠ Q RS  [Each being 90°]

  3. S R is common.

→ ΔP SR ≅  Δ Q RS → [Side-Angle-Side Congruency]

∴ PR =Q S [ corresponding part of congruent triangles ]

Hence proved.