Question

Find the value of x such that PQ = PR where P, Q and R
are the points (2, 5), (x, -3) and (7, 9) respectively.​

Answer 1

Answer:

Given: ABCD is a square.

thus, AB=BC

AP=BQ (Given)

AB−AP=BC−BQ

PB=CQ (I)

Now, In △PBQ and △CQR,

∠PBQ=∠QCR (Each 90

∘

)

PB=CQ (From I)

BP=CR (Given)

thus, △PBQ≅△CQR (SAS rule)

or, PQ=QR (By cpct)

Now, In △PQR

PQ=QR

thus, ∠PRQ=∠QPR=x (Isosceles triangle property)

∠PQR=90

∘

(Given)

Sum of angles = 180

∠PQR+∠QPR+∠QRP=180

90+x+x=180

2x=90

x=45

Thus, ∠PRQ=45

Step-by-step explanation:

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