Question

Congruence of triangles. Class 7

Answer 1

Step-by-step explanation:

1.

(ii) Yes, ∆PQS is congruent to ∆PRS.

IN ∆PQS AND ∆PRS,

PQ=RS

PS=QR [ SINCE ITS A PARALLELOGRAM AND OPPOSITE SIDES ARE EQUAL]

PR=PR[COMMON SIDE TO BOTH TRIANGLES]

Therefore by SSS congruency criterion-

∆PQS is congruent to ∆PRS

(iii) Yes, Angle Q = Angle S [by corresponding parts of congruent triangles(CPCT)]

(i) The three pairs of equal parts are,

PS and QR

PQ and RS

PR and PR ( it's common to both the triangles)

2.

(i) AO=OB and

CO=OD[Since AB and CD bisect each other]

Angle AOC = Angle BOD( vertically opposite angles)

(ii)∆AOC=~ ∆ BOD

(iii) Yes, AC=BD ( by corresponding parts of congruent triangles)

Hope it's helpful .