Question

In a parallelogram PQRS, PQ=12 cm and PS=9 cm.The bisector of Angle P meets SR in M. PM and QR when produced meet at T. Find the length of RT​

Answer 1

Step-by-step explanation:

Firstvplease refer to the image

In the parallelogram angle bisector of "angle P" is meeting SR at M and when the lines PM and QR are extended they meet at T

Now to find RT first we proof that

Angel QPM = Angel SPM. ------( GIVEN) ( i )

ANGEL SPT = Angel QTP ------- ( alternate interior) ( ii )

therefore from 1 and 2 we get

ANGEL QOT = ANGEL QTP

this proces that Triangle QPT is Isosceles Triangle

and

PQ = QT = 12

PQ = QT + RT

PQ = 12

QR = 9

12 = 9 + RT

RT = 12 - 9

RT = 3 cm

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