Question

In the given figure, PQ=QR and angleX=angleY. Prove that AR=PB.

Answer 1

Answer:

by opposite angles are so it is equal

Step-by-step explanation:

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Answer 2

Answer:              Sol: In the given figure,

<QAR + < PAR = 180° (linear pair)

<QAR + x = 180°

<QAR = 180° - x -------- (i)

Similarly, <QBP + <RBP = 180°

<QBP + y = 180°

<QBP = 180° - y ------- (ii)

But given, < x = < y

⸫ <QAR = < QBP [ () ()]

In ΔQAR and ΔQBP,

Given, (i) QR=PQ

(ii) <QAR = < QBP (from the above prove)

(iii) <Q = <Q (common)

⸫ By AAS congruence, Δ QAR ≅ Δ QBP

And by CPCT, AR = PB (Proved)