Question

in the adjoining figure OP = Oq and angle OPX = angleOQY Prove that ∆ OPX congruent to ∆ OQY and pX = QY​

Answer 1

Step-by-step explanation:

OP=OQ( GIVEN)

< P= <Q

<POX=<QOY

∆ OPX is congruent to∆ OQY

px=qy (cpct)

Answer 2

Answer:

It is given that OA=OB and OP=OQ

By considering the △OAQ and △OPB

Therefore, by SAS congruence criterion

△OAQ=△OPB

We know that the corresponding parts of congruent triangles are equal

So we get

∠OBP=∠OAQ..(1)

Consider △BXQ and △PXA

We can write it as

BQ=OB−OQ and PA=OA−OP

We know that OP=OQ and is given that OA=OB

So we get BQ=PA.(2)

In △BXQ and △PXA

We know that ∠BXQ and ∠PXA are vertically opposite angles

∠BXQ=∠PXA

From (1) and (2) and AAS congruence criterion we get

△BXQ≅△PXA

So we get PX=QX and AX=BX(c.p.c.t).