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Triangles — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsTriangles4 Marks
Question
For the following statments state whether true$(T)$ or false$(F):$
In a $\triangle\text{ABC},\text{AB}=6\text{cm},\angle\text{A}=45^\circ$ and $\text{AC}=8\text{cm}$ and in a $\triangle\text{DEF},\text{DF}=9\text{cm},\angle\text{D}=45^\circ$and $\text{DE}=12\text{cm},$ then $\triangle\text{ABC}\sim\triangle\text{DEF}.$
✓

Answer

False.
Solution:
Given that,
$\angle\text{A}=45^\circ,\text{AB}=6\text{cm}$ and $\text{AC}=8\text{cm}$
$\angle\text{D}=45^\circ,\text{DF}=9\text{cm}$ and $\text{DE}=12\text{cm}$
Consider, $\triangle\text{ABC}$ and $\triangle\text{DFE},$
$\angle\text{A}=\angle\text{D}=45^\circ$
$\frac{\text{AB}}{\text{DE}}=\frac{6}{12}=\frac{1}{2}$
$\frac{\text{AC}}{\text{DF}}=\frac{8}{9}$
$\Rightarrow\frac{\text{AB}}{\text{DF}}\not=\frac{\text{AC}}{\text{DF}}$
Thus, the triangles are not similar.

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