Question

prove that corresponding medians of two similar triangles are proportional to corresponding sides of a triangle pls Give answer urgentlyI need answer very much

Answer 1

Hello mate,

Here is your answer,

Answer 2

Solution:

As, given two Triangles are Similar

Consider two Triangles

ΔABC~ΔP QR

When triangles are similar their Corresponding sides are proportional and Corresponding interior angles are equal.

$\frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}$  

∠A=∠P, ∠B=∠Q, ∠C=∠R

In ΔAB D and ΔP Q S

AD and PS are medians.

So, B D = D C and , Q S= S R

$\frac{AB}{PQ}=\frac{BD}{QS}$ →→ [ΔABC~ΔP QR]

∠B=∠Q→→→ΔABC~ΔP QR

ΔAB D ~ ΔP Q S→→→[SAS]

$\frac{AB}{PQ}=\frac{AD}{PS}=\frac{BD}{QS}$

$\frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}=\frac{AD}{PS}$