ABD - PQS and AD and PS are the medians- then

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Standard X

Mathematics

SAS Similarity

ABD ∼ PQS and...

Question

$△ A B D \sim △ P Q S$ and AD and PS are the medians, then

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Solution

If $△ A D B \sim △ P S Q$ ,

$\frac{A B}{P Q} = \frac{A D}{P S} = \frac{B D}{Q S}$
(corresponding sides of similar triangles will be in same ratio)

$∠ B = ∠ Q$ (corresponding angles of similar triangles will be equal)

$\Rightarrow \frac{A B}{P Q} = \frac{2 B D}{2 Q S} = \frac{B C}{Q R}$

Now, consider $△ A B C$ and $△ P Q R$ .

$∠ B = ∠ Q$
$\Rightarrow \frac{A B}{P Q} = \frac{B C}{Q R}$

$∴ △ A B C \sim △ P Q R$ (by SAS similarity criterion)

$\frac{A C}{P R} = \frac{B C}{Q R} = \frac{A B}{P Q}$
$\Rightarrow \frac{A C}{B C} = \frac{P R}{Q R}$

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Similar questions

In the following figure, the sides AB and BC and the median AD of triangle ABC are respectively equal to the sides PQ and QR and median PS of the triangle PQR. Prove that $Δ$ PQR are congruent.

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. In

Δ P Q R

, PS and RT are medians and SM || RT Then PQ =

△ 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}

In the figure, PN, and RT are medians of $△$ PQR and NM || RT. Prove that $Q M = \frac{1}{4} P Q$ .

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△ABD∼△PQS and AD and PS are the medians, then

$△ A B D \sim △ P Q S$ and AD and PS are the medians, then