Question

1 . If the diagonals of a parallelogram are equal then show that it is a rectangle.

2 . Show that if the diagonals of a quadrilateral by bisect each other at a right angles then it is a rhombus.

3 . Show that diagonals of a square are equal and bisect each other at right angles .

4 . Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles then it is a square .
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Please draw on paper show it properly and neatly.

Answer 1

Answer:

Refer to the picture attached, it will be helpful.

Step-by-step explanation:

Answer for Questions 1)

Given,

ABCD is a parallelogram where the Diagonals AC and BD are equal so,

AC=BD

To Prove:

ABCD is a rectangle

Proof:

In Δ ABC and ΔDCB

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

BC=BC (Common)

AC= DB (Given)|

So, ΔABC ≅ ΔDCB By SSS rule of congruency.

Therefore, ∠ABC = ∠DBC by CPCT

Now,

AB║DC (Opposite sides of a parallelogram are parallel)

and BC is transversal.

So, ∠B + ∠C = 180 ° ( Interior angles on the same side of a transversal are supplementary)

Since ∠ABC=∠DBC,

∠B + ∠B = 180°

So, 2B= 180°

⇒B= 180/2 = 90°

Since one of the angles of the parallelogram is 90°,

Hence it's a rectangle

Answer 2

Answer:

nice answer given by the person