Sides AB and AC and median AD of a triangle ∆ABC are respectively pr

1.	Sides AB and AC and median AD of a triangle ∆ABC are respectively proportional to sides PQ and PR and mediam PM of another triangle ∆PQR. Show that ∆ABC ~ ∆PQR.
Answer» Data: Sides AB and AC and median AD of a triangle ∆ABC are respectively proportional to sides PQ and PR and median PM of another triangle ∆PQR. To Prove: ∆ABC ~ ∆PQR In ∆ABC and ∆PQR \(\frac{AB}{PQ} = \frac{AC}{PR} = \frac{AD}{PM}\) Corresponding sides are proportional. Similarity criterion for ∆ is S.S.S ∴ ∆ABC ~ ∆PQR.

Sides AB and AC and median AD of a triangle ∆ABC are respectively proportional to sides PQ and PR and mediam PM of another triangle ∆PQR. Show that ∆ABC ~ ∆PQR.

Answer»

Data: Sides AB and AC and median AD of a triangle ∆ABC are respectively proportional to sides PQ and PR and median PM of another triangle ∆PQR.

To Prove: ∆ABC ~ ∆PQR

In ∆ABC and ∆PQR

\(\frac{AB}{PQ} = \frac{AC}{PR} = \frac{AD}{PM}\)

Corresponding sides are proportional.

Similarity criterion for ∆ is S.S.S

∴ ∆ABC ~ ∆PQR.