1) ,
,
(given)
2) is a right angle (perpendicular lines form right angles)
3) and
are right triangles (a triangle with a right angle is a right angle)
4) (HL)
5) (CPCTC)
Given: Quadrilateral PQRS is a rectangle. Prove: PR = QS
1 answer:
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.
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