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# 1).If the areas of two similiar traingles are equal, prove that they are congruent.

Asked by 12th October 2013, 11:39 PM
Let the two triangles be ABC and DEF.
Also assuming that the area (ABC) ~ area (DEF)  [Similar]

So, area (ABC) / area (PQR) = (AB / PQ)2 = (BC / QR)2 = (AC / PR)2

Given in the question stem that area (ABC) = area (PQR)

=> Area (ABC) / Area (PQR) = 1

Hence, 1 =  (AB / PQ)2 = (BC / QR)2 = (AC / PR)2

Now taking the square on both sides in the above equation, we get:

1 = (AB / PQ) = (BC / QR) = (AC / PR)

So, AB = PQ, BC = QR and AC = PR

Hence, triangle ABC is congruent to the triangle PQR.
Answered by Expert 14th October 2013, 10:16 AM
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