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Maharashtra Class 10 Answered

If the area of two similar triangles are equal then prove that they are congruent
Asked by nomansayyed78622 | 11 Mar, 2019, 09:25: PM
answered-by-expert Expert Answer
Let Δ ABC and Δ PQR are similar triangles. 
 
hence we have sides are in same ratio,  i.e.,   AB = k PQ  ,  AC = k PR  ,  BC = k QR 
 
Since Δ ABC and Δ PQR are similar , altitude AD and PS are also in same ratio.  AD = k PS
 
Area of Δ ABC = (1/2) BC × AD = (1/2) (k QR ) (k PS)   = k2 ΔPQR
 
but we are given that Δ ABC = Δ PQR ,  hence k2 = 1  or  k = 1
 
hence , AB =  PQ  ,  AC = PR  ,  BC = QR   and both triangles are congruent
Answered by Thiyagarajan K | 12 Mar, 2019, 09:02: AM

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