Sides $AB$ and $BC$ and median $AD$ of a $△ABC$ are respectively proportional to sides $PQ$ and $PR$ and median $PM$ of $△PQR$. Show that $△ABC ∼ △PQR$.

Question

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- Let $ \triangle ABC $ and $ \triangle PQR $ be two triangles such that the sides $ AB \parallel PQ $, $ BC \parallel PR $, and $ AD \parallel PM $. - Since the corresponding sides are proportional, we can use the criteria for similarity of triangles: $$ \frac{AB}{PQ} = \frac{BC}{PR} = \frac{AD}{PM} $$ - Therefore, by the Side-Side-Side (SSS) similarity criterion, $ \triangle ABC \sim \triangle PQR $.

Sides $AB$ and $BC$ and median $AD$ of a $△ABC$ are respectively proportional to sides $PQ$ and $PR$ and median $PM$ of $△PQR$ . Show that $△ABC ∼ △PQR$ .

Solution and Explanation

Top Questions on Triangles

Questions Asked in CBSE X exam

Notes on Triangles

Sides ABABAB and BCBCBC and median ADADAD of a △ABC△ABC△ABC are respectively proportional to sides PQPQPQ and PRPRPR and median PMPMPM of △PQR△PQR△PQR. Show that △ABC∼△PQR△ABC ∼ △PQR△ABC∼△PQR.

Solution and Explanation

Top Questions on Triangles

Questions Asked in CBSE X exam

Notes on Triangles

Sides $AB$ and $BC$ and median $AD$ of a $△ABC$ are respectively proportional to sides $PQ$ and $PR$ and median $PM$ of $△PQR$ . Show that $△ABC ∼ △PQR$ .