Question

abcd is a quadilateral in which ad =bc . if p q r s are the midpoints of sides ab, ac , cd ,bd show that pqrs is a rhombus

Answer 1

Related Question

ABCD is Rectangle in which P,Q,R,S is a mid point . show that PQRS is rhombus.

$sr || ac \: sr = 1\%2ac \: \: by \: mid \: point \: theoram \\ \: \: \: \: \: \: \: ...1 \\ pq || ac \: pq = 1\%2ac \: \: by \: mid \: point \: theorm \\ \: \: \: \: \: \: \: .....2 \\ from \: equation \: 1 \: and \: 2 \\ pqrs \: is \: a \: || gm$

$sp || db \: \: \: sp = 1\%2db \: \: \: \: by \: mid \: point \: theoram$

As we all know that diagonals of rectangle are equal

AB=DB

1%2AC=1%2DB

PQ=SP From equation 2 and 3

ABCD is parallelogram in which adjacent side equal equal so that PQRS is rhombus