Q. 253.7( 3 Votes )

# Diagonals of para

Answer :

(i) *OB* = *OD*

*OB = OD [In a parallelogram diagonals bisect each other]*

(ii) ∠*OBY* =∠*ODX [Alternate interior angles are equal]*

(iii) ∠*BOY*= ∠*DOX* *[Vertically opposite angles are equal]*

(iv) Δ*BOY* ≅ Δ*DOX*

*In ΔBOY and ΔDOX*

*OB = OD [In a parallelogram diagonals bisect each other]*

∠*OBY* =∠*ODX [Alternate interior angles are equal]*

∠*BOY*= ∠*DOX* *[Vertically opposite angles are equal]*

Δ*BOY* ≅Δ*DOX [ASA rule]*

Now, state if *XY* is bisected at *O*.

*Hence OX = OY [Corresponding parts of congruent triangles]*

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