Question

If two consecutive angles of a parallelogram are congruent what type of quadrilateral
is the given parallelogram?
1) Square
2) Rectangle
3) Rhombus
4) All of these.​

Answer 1

Answer:

D is the answer of this question

Answer 2

Given : two consecutive angles of a parallelogram are congruent

To Find : what type of quadrilateral is the given parallelogram

1) Square

2) Rectangle

3) Rhombus

4) All of these.​

Solution:

Parallelogram has opposite sides equal

opposite angles equal

sum of adjacent angles = 180°

Let say ABCD is a parallelogram

AB = CD

BC = AD

∠A = ∠C  and ∠B = ∠D

∠A  + ∠B =  ∠C + ∠D = 180°

given that  two consecutive angles of a parallelogram are congruent

=> ∠A  = ∠B   = ∠C = ∠D

=> ∠A  = ∠B   = ∠C = ∠D  = 90°

Now each angle = 90°

and opposite sides are equal

Hence this is a rectangle

the given parallelogram is rectangle

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