Question

If the diagonals of a parallelogram are equal, then show that it is a rectangle​

Answer 1

Step-by-step explanation:

1. The opposite angles of a parallelogram are equal.
2. The opposite sides of a parallelogram are equal.
3. The diagonals of a parallelogram bisect each other

Answer 2

Figure:-

Given:-

• The diagonals of a parallelogram are equal.

Solutions:-

• Let ABCD be a parallelogram.

To Show:-

• Let ABCD be a rectangle.

Prove that:-

• One of its interior angle.

In ∆ABC and ∆DCB,

AB = DC (Opposite sides of a parallelogram are equal)

BC = BC (Common)

AC = DB (Given)

.:. ∆ABC ~ ∆DCB (By SSS Congruence rule)

<ABC ~ <DCB

The sum of the measures of angle on the same side of transversal is 180°

<ABC + <DCB = 180° (AB//CD)

<ABC + <ABC = 180°

2<ABC = 180°

<ABC = 180°/2

<ABC = 90°

Hence, ABCD is a parallelogram and one of its interior angle is 90°, ABCD is a rectangle.