$△ A B C \sim △ P Q R$ . If AD and PM are corresponding medians of the two triangles , then $\frac{A B}{P Q} = \frac{A D}{P M}$ .

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Solution

Given: $△ A B C \sim △ P Q R$
$\frac{A B}{P Q} = \frac{B C}{Q R} = \frac{A C}{P R}$ (Corresponding sides)
or $\frac{A B}{P Q} = \frac{\frac{1}{2} B C}{\frac{1}{2} Q R}$
$∠ A B C = ∠ P Q R$ (Corresponding angles)
Now, AD and PM are medians of $△ A B C$ and $△ P Q R$ respectively,
thus, in $△ A B D$ and $△ P Q M$
$∠ A B D = ∠ P Q M$ (Since, $△ A B C \sim △ P Q R$ )
$\frac{A B}{P Q} = \frac{B D}{Q M}$ (AD and PM are medians)
Thus, $△ A B D \sim △ P Q M$ (SAS rule)
Hence, $\frac{A B}{P Q} = \frac{A D}{P M}$

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Similar questions

Triangle ABC is similar to triangle PQR. If AD and PM are corresponding medians of the two triangles, prove that : $\frac{A B}{P Q} = \frac{A D}{P M}$ .

State true or false:

Triangle

A B C

is similar to triangle

P Q R

. If

A D

and

P M

are corresponding medians of the two triangles. Then,

\frac{A B}{P Q} = \frac{A D}{P M} .

If $Δ A B C \sim Δ P Q R$ and AD and PM are corresponding medians of the two triangles, then

Q. If

A D

and

P M

are medians of triangles

A B C

and

P Q R,

respectively where

△ A B C \sim △ P Q R

, prove that

\frac{A B}{P Q} = \frac{A D}{P M}

Q. Question 16
If AD and PM are medians of triangles ABC and PQR, respectively where

Δ A B C \sim Δ P Q R

. Prove that

\frac{A B}{P Q} = \frac{A D}{P M}

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△ABC∼△PQR. If AD and PM are corresponding medians of the two triangles , then ABPQ=ADPM.

$△ A B C \sim △ P Q R$ . If AD and PM are corresponding medians of the two triangles , then $\frac{A B}{P Q} = \frac{A D}{P M}$ .