Question

Let $\square$PQRS be a rhombus. O be any point on the diagonal QS. Prove that seg OP $\cong$ seg OR.

Answer 1

In $△$OTP and $△$OTR
seg PT $\cong$ seg TR (Diagonals of a rhombus bisect each other)
$\angle$OTP = $\angle$OTR = 90$°$ (Diagonals of a rhombus perpendicularly bisect each other)
seg OT $\cong$seg OT (common)


So, By SAS congruency criteria,
$△$OPT $\cong$ $△$ORT
seg OP $\cong$ seg OR (by c.a.c.t)