Question

If the diagonals of a parallelogram are equal it is a rectangle

Answer 1

Answer:

Step-by-step explanation:

Given that the diagonals AC and BD of parallelogram ABCD are congruent.

Consider triangles ABD and ACD.

AC = BD [Given]

AB =  DC [opposite sides of a parallelogram]

AD = AD [Common side]

∴ ΔABD ≅ ΔDCA [SSS congruence criterion]

∠BAD = ∠CDA [CPCT]

∠BAD + ∠CDA = 180° [Adjacent angles of a parallelogram are supplementary.]

So, ∠BAD and ∠CDA are right angles as they are congruent and supplementary.  

Therefore, parallelogram ABCD is a rectangle since a parallelogram with one right interior angle is a rectangle

Answer 2

Step-by-step explanation:

Given,

ABCD is a llgm

AB=DC

AC and BD are diagonals

To prove that: ABCD is a rectangle

Proof: In triangles ADC and DAB

AD = AD (Common side)

AC = DB (Diagonals given)

AB = DC (Given)

∆ADC congruent to ∆DAB by SSS congruency