If the area of two similar triangles are equal, prove that they are congruent
Triangles (10)If the area of two similar triangles are equal, prove that they are congruent.
Answer
Let ΔABC ~ ΔPQR.
$\frac{ar\triangle ABC}{ar\triangle PQR} = \frac{AB^2} {PQ^2} = \frac{BC^2} {QR^2} = \frac{AC^2} {PR^2}$
Given ar ΔABC = ar ΔPQR
$\frac{AB^2} {PQ^2} = 1 = \frac{BC^2} {QR^2} = \frac{AC^2} {PR^2}$
AB = PQ, BC = QR, AC = PR
Therefore, ΔABC $\cong$ ΔPQR. (sss congruence rule)
Exam Year:
2018
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