Question

Prove that rhombus with one angle 90 degree is a square

Answer 1

In a rhombus,alternate angles are equal.

lets say in a rhombus abcd,angle A=90 degree.

therefore angle C is also 90 degree.

angle D=angle B(let it be x)

sum of angles in a rhombus=360 degree.

therefore,90+90+x+x=360

therefore,2x=180

therefore,x=90 degree

hence proved

Answer 2

Step-by-step explanation:

As we know that opposite angles of the rhombus are equal therefore 2 angles are 90...( i.e. the given one and opposite to it)

let the other 2 angles be x

now

x+x+90+90=360

2x=180

x=90

therefore the required angles of the rhombus are 90,90,90,90 and we know that all the sides of the rhombus are equal...hence it is a square..