Question

3 ABCD is a thombus RABS is a straight line such that RA = AB = BS
Prove that: RD and SC when produced meet at right angle.​

Answer 1

According to the statement, the figure will be in alongside, in which RD and SC produced meet at point P.

Also , RA=AB=BS=BC=CD=DA

As to prove <P = 90⁰

proof : In triangle RAD , RA = AD → <R = <ADR = x(let)

and, exterior angle DAB = <R + <ADR = x + x = 2x.

In triangle SBC, BS = BC → <S = <BCS = y(let)

and, exterior angle ABC = <S + <BCS = y + y = 2y

Since the adjacent angles of a rhombus are supplementary.

i.e. <DAB + <ABC = 180⁰ → 2x + 2y = 180⁰ and x+y=90⁰

i.e. <R + <S = 90⁰ → <P = 180⁰– 90⁰= 90⁰

HENCE PROVED