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
Related Questions
- Given $\Delta ABC \sim \Delta PQR$, if $\frac{AB}{PQ} =\frac{1}{3}$
- In the adjoining figure, A, B and C are points on OP, OQ and OR
- Two right triangles ABC and DBC are drawn on the same hypotenuse BC
- Prove that the area of an equilateral triangle described on one side of the square is equal
- In an equilateral $\triangle$ ABC, D is a point on side BC such that BD
- Observe the figures given below carefully and answer the questions