Question

if PM and RN are perpendicular on the diagonal QS of a parallelogram PQRS.Prove that triangle PMS=~triangle RNQ​

Answer 1

Triangle PMS ≅ Triangle RNQ

GIVEN: PM and RN are perpendicular on the diagonal QS of a parallelogram PQRS.
TO PROVE: Triangle PMS ≅ Triangle RNQ
SOLUTION:​

As we are given in the question,

PM and RN are perpendicular on the diagonal QS of a parallelogram PQRS.

According to the question,

In △PMS & △RNQ,

∠PMQ=∠RNQ  (each 90°)

PS=RQ (opposite sides of the parallelogram)

∠MSP=∠NQR (Alternate angle)

∴△PMS≅△RNQ

Hence Proved.

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Answer 2

Answer:

triangle PMS ≅ triangle RNQ

GIVEN: A parallelogram PQRS has PM and RN perpendicular on its diagonal (QS).

Triangle PMS Triangle RNQ SOLUTION IS PROVEN TO BE TRUE.

As stated in the question,

On the diagonal QS of a parallelogram PQRS, PM and RN are perpendicular.

In response to the query,

In △PMS and △RNQ,

△PMQ = △RNQ (each at 90°)

PS=RQ (opposite sides of the parallelogram)

∠MSP=∠NQR (Alternate angle)

∴△PMS≅△RNQ

So it is Proven.

Additional information:

A four-sided, parallel, and equal plane figure having opposite sides.

By connecting the opposite vertices of a parallelogram with a segment, a parallelogram may always be divided into two identical triangles. Conversely, no matter what kind of triangle is used, two identical copies of a triangle may always be assembled to produce a parallelogram.

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