In the diagram below, mnpq is a parallelogram whose diagonals are perpendicular. prove: mnpq is a rhombus.

Given : MNPQ is a parallelogram whose diagonals are perpendicular.

To prove :  MNPQ is a rhombus.

Proof:

In parallelogram MNPQ,

R is the intersection point of the diagonals MP and NQ( shown in below diagram)

(Because, the diagonals of parallelogram bisects each other)

(Right angles )

 (Reflexive)

Thus, By SAS postulate of congruence,

By CPCTC,

Similarly,

We can prove,

By CPCTC,

But, By the definition of parallelogram,

and

⇒

All four side of parallelogram MNQP are congruent.

⇒ Parallelogram MNPQ is a rhombus.

Hence, proved.

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it