Question

I'm the given figure, PQ and pS bisect each other at O. show that

a. triangle pqr =~ QOS.
b. pR=~QS.
c. pR||QS
​

Answer 1

Answer:

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Given: PQ and PS bisect each other at O.

To prove : PQR ≌ QOS, PR ≌QS and PR ||QS.

Proof :

a. In POR and QOS,

PO= OQ (O is the mid- point of PQ)

RO = OS ( o is the mid - point of RS)

and <POQ ≌<QOS ( vertically opposite angle )

Therefore, POQ ≌ QOS. (By SAS congruent criterion )

b. PR ≌ QS ( Corresponding parts of congruent criterien)

c. PR and QS are two line segment and PQ is a transversal.

since POR ≌ QOS, the corresponding of vertices in these two congruent triangles is P ⟷ Q, O ⟷O and R ⟷S.

Thus, ≺OPR = ≺OQS.

But these angles from a pair of alternate interior angles.hence,PR|| QS.

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