Hello, waterqueen7!

Here's one approach . . .

Q 4. Rajan constructed rhombus ABCD.

He then drew a straight line RABS such that RA = AB = BS.

Prove that RD and SC when produced meet at a right angle. Code:

Q
*
* *
* *
D*-----------*C
*α/ /β*
* / / *
* / / *
*α /θ /θ β*
* - - - - *-----------* - - - - *
R A B S

We have: .

Let

.Then: .

In isosceles , let: .

Since the sum of its angles is 180°: . .**[1]**

In isosceles , let: .

Since the sum of its angles is 180°: . .**[2]**

In

Substitute [1] and [2]: .

Therefore: . is a right angle.