ICSE Class 10 Answered
1).If the areas of two similiar traingles are equal, prove that they are congruent.
Asked by | 12 Oct, 2013, 11:39: PM
Expert Answer
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
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 | 14 Oct, 2013, 10:16: AM
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