Question

in quadrilateral ABCD ,AD= CD and angle A = 90 degree = angle C. Prove that AB=BC

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Answer 1

REF.Image

→ In △ABD & △BCD

AD=CD (Given) (Height)

BC=BC (Common) (Hypotenuse)

∠BAD=∠BCD (right angles)

∴△BAD≅△BCD (By RHS congruency Rule)

∴A B=BC ( By CPCT)

Answer 2

Answer:

Given: In ABCD, AB=CD, ∠A=∠C=90°

To Prove: AB = BC

Proof:

Statement. Reason

In △ABD and △BCD,

1. ∠A=∠C. Given (90° each)

2. BD=BD. Common side

3. AD = CD. Given

∴ △ABD≅△BCD (By RHS congruency rule)

∴ AB = BC (CPCT)

Hence proved, AB = BC.