prove that
OC OD
6. If the areas of two similar triangles are equal, then show that triangles are congruent
7. ABCD is a trapezium in which ABIDC and its diagonals intersect each other at O. Prow
Answers
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Answer:
Step-by-step explanation:
If the areas of two similar triangles are equal, then show that triangles are congruent
Let say
ΔABC ≅ Δ XYZ
=> AB/XY = BC/YZ = CA/ZX = K
=> AB = K * XY
BC = K * YX
CA = K * ZX
S for ΔABC = (AB + BC + CA)/2
Area of ΔABC = √S(S-AB)(S-BC)(S-CA)
=>Area of ΔABC = √((AB + BC + CA)/2)((BC + CA-AB)/2)((AB + CA-BC)/2)((AB + BC-CA)/2)
AB = K * XY , BC = K * YX & CA = K * ZX
=> Area of ΔABC = √(K(XY + YZ +ZX)/2)(K(YZ + ZX- XY)/2)(K(XY + ZX-YZ)/2)(K(XY + YZ-ZX)/2)
=> Area of ΔABC = K²√((XY + YZ +ZX)/2)((YZ + ZX- XY)/2)((XY + ZX-YZ)/2)((XY + YZ-ZX)/2)
=> Area of ΔABC = K²Area of ΔXYZ
while it is given Area of ΔABC = Area of ΔXYZ
=> Area of ΔXYZ = K²Area of ΔXYZ
=> 1 = k²
=> k = 1
AB = XY , BC = YZ & CA = ZX
Hence ΔABC & ΔXYZ are congruent
If the areas of two similar triangles are equal, then triangles are congruent