Question

question 19 plsssss ans

Answer 1

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Answer 2

(1)PB = QC
We know that AB = BC
also AP = BQ
thereby, we can say that,
AB - AP = BC - BQ
PB = QC
thus proved.

(2) PQ = QR
Now consider ΔPBQ, ΔRCQ
PB = QC
Angle B = Angle C
BQ = CR
So ΔPBQ and ΔRCQ are congruent under SAS congruency criteria.
Therefore PQ = QR [CPCT]

(3) <QPR = 45'
in ΔPQR
<Q = 90'
And PQ = QR
So Δ PQR is isosceles triangle.
Therefore <P = <R
From angle sum property,
<P + <Q + <R = 180
= 2<P + 90' = 180 [ by taking <P =<R, < A = 90]
= 2<P = 90'
=<P = 45'
Thus proved that <QPR = 45'

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