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Triangles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsTriangles5 Marks
Question
Two triangles ABC and PQR are such that AB = 3cm, AC = 6cm, $\angle\text{A}=70^\circ,\text{PR}=9\text{cm},\angle\text{P}=70^\circ$ and $\text{PQ}=4.5\text{cm}.$ show that $\triangle\text{ABC}\sim\triangle\text{PQR}$ and state the similarity criterion.
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Answer


In $\triangle\text{ABC}$ and $\triangle\text{PQR},$
$\angle\text{A}=\angle\text{P}=70^\circ\ ...\ \text{(Given)}$
$\frac{\text{AB}}{\text{PQ}}=\frac{3}{4.5}=\frac{2}{3}$
$\frac{\text{AC}}{\text{PR}}=\frac{6}{9}=\frac{2}{3}$
$\Rightarrow\frac{\text{AB}}{\text{PQ}}=\frac{\text{AC}}{\text{PR}}$
so, $\triangle\text{ABC}\sim\triangle\text{PQR}$ ...(SAS criterion for similarity)

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