Question

In a quadrilateral ABCD,AB=AD and BC=DC,then show that the diagonals AC and BD intersect each other at right angle​

Answer 1

Answer:

diagonals AC and BD intersect each other at right angle​

Step-by-step explanation:

in Δ ABC   & ΔADC

AB = AD   - Given

BC = DC   - Given

AC = AC  ( common)

=>  Δ ABC ≅ ΔADC

=> ∠CAD = ∠CAD

Let say Diagonal intersect at O

then ∠OAD = ∠OAB

now in Δ AOD  & ΔAOB

AO = AO  ( common)

AD = AB  ( given)

∠OAD = ∠OAB  ( already proved)

=> Δ AOD  ≅ ΔAOB

=> ∠AOD = ∠AOB

∠AOD +  ∠AOB = 180°  ( straight LIne)

=> ∠AOD = ∠AOB = 90°

Similarly

we can show that

∠COD = ∠COB = 90°

Hence Proved that  diagonals AC and BD intersect each other at right angle​