Question

PQRS is a rhombus with diagonal PR which is extended to a point T. Prove that TQ= TS

Answer 1

Answer:

TQ = TS

Step-by-step explanation:

PQRS is a rhombus with diagonal PR  & QS

we know diagonals of a rhomus perpendicularly bisect each other

Let say intersection point PR & QS = O

so OQ = OS  and ∠ ROS = ∠ROQ = 90°

now PR extended to T

now in Δ OTS  

∠TOS = 90°   as ∠ ROS = 90°  & T is point on Extended PR

=> TS² = OT² + OS²

Similarly

in Δ OTQ

TQ² = OT² + OQ²

OS = OQ

=>  TQ² = OT² + OS²

=> TQ² = TS²

=> TQ = TS