Question

Prove that :

Prove that the ratio of the areas of Two similar Δ is equal to the ratio of the squares of their corresponding angle bisector segments. ​

Answer 1

Answer:

Step-by-step explanation:

Consider two triangles ABC and DEF.

AX and DY are the bisectors of the angles A and D respectively.

Ratio of the areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides.

So,Area (ΔABC) / Area (ΔDEF) = AB2/ DE2-----(1)

ΔABC ~ ΔDEF ⇒ ∠A = ∠D1/ 2 ∠A = 1 / 2 ∠D ⇒ ∠BAX = ∠EDY

Consider ΔABX and ΔEDY∠BAX = ∠EDY∠B = ∠E

So, ΔABX ~ ΔEDY [By A-A Similarity]

AB/DE = AX/DY⇒ AB2/DE2= AX2/DY2-- (2)

From equations (1) and (2),

we getArea (ΔABC) / Area (ΔDEF) = AX2/ DY2

Hence proved.

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Answer 2

$\textbf{Answer is in Attachment !}$