Question

In ∆ABC , AB²+ BC²= AC2²
and in ∆PQR , AngleQ = 90°
and AB = PQ , BC = QR .
Prove: Angle B=90°.​

Answer 1

Answer:

In triangle ABC and triangle PQR,we have

BC=QR......................................................1

angleA=90°

angleC=angleR=40°...............................2

and angleQ=50°

In triangle PQR by angle sum property we have,

angleP+angleQ+angleR=180°

anglep+50°+40°=180° (by eq2)

angleP=90°=angleA...........................3

In triangleABC by angle sum property we have,

angleA+angleC+angleB=180

90°+40°+angleB=180

angleB=50°=angleQ...........................4

By eq1,eq3,eq4 we get,

tringleABC congruent to triangle PQR by

ASA criterion rule i.e angle side angle.

Step-by-step explanation:

Answer 2

Answer:

In triangle ABC and triangle PQR,we have

BC=QR......................................................1

angleA=90°

angleC=angleR=40°...............................2

and angleQ=50°

In triangle PQR by angle sum property we have,

angleP+angleQ+angleR=180°

anglep+50°+40°=180° (by eq2)

angleP=90°=angleA...........................3

In triangleABC by angle sum property we have,

angleA+angleC+angleB=180

90°+40°+angleB=180

angleB=50°=angleQ...........................4

By eq1,eq3,eq4 we get,

tringleABC congruent to triangle PQR by

ASA criterion rule i.e angle side angle.

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