Math, asked by AngelPriyaFB, 5 months ago

Q9. If the diagonals of a parallelogram are equal in length, show that the parallelogram is a rectangle.​

Answers

Answered by wtfhrshu
54

Given: ABCD is a parallelogram whose diagonals are AC and BD and AC = BD.

Need to prove: ABCD is a rectangle

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

☯︎ In ∆ABC and ∆ABD,

AB = AB (Common)

BC = AD (Opposite sides of a parallelogram)

AC = BD (Given)

∴ ∆ABC ≅ ∆ABD (SSS axiom)

So, ∠ABC = ∠BAD (c.p.c.t)

But, ∠ABC + ∠BAD = 180° (Co-interior angles)

∴ ∠ABC = ∠BAD = 90°

Hence, a parallelogram whose each angles are 90° is a rectangle.

Similar questions