Question

In the given pairs of similar triangles, write the corresponding vertices, corresponding sides and their ratios.

Answer 1

(a) From figure, $△ABC$ and $△DEF$,

$\angle BAC=\angle FDE;\angle ABC=\angle DEF$ and $\angle ACB=\angle DFE$

$\frac{DE}{AB}=\frac{1}{2};\frac{DC}{AC}=\frac{1}{2};\frac{FE}{BC}=\frac{1}{2}$

$\frac{ar\left(△DEF\right)}{ar\left(△ABC\right)}={\left(\frac{DE}{AB}\right)}^2+{\left(\frac{DC}{AC}\right)}^2+{\left(\frac{FE}{BC}\right)}^2={\left(\frac{1}{2}\right)}^2$

$\Rightarrow \frac{ar(△DEF}{ar\left(△ABC\right)}=\frac{1}{4}$

(b) $AB\parallel PQ$

$\therefore \angle ACB=\angle PCQ$ ...... [Vertically opposite angle]

$3\left(△ABC\right)=△PCQ$

i.e, $\frac{AB}{PQ}=\frac{AC}{CQ}=\frac{CB}{PC}=\frac{1}{3}$

(c) $\frac{KL}{XY}=\frac{LM}{YZ}=\frac{KM}{XZ}=\frac{1}{2}$

$\Rightarrow \angle KML=\angle XZY$

$\angle MKL=\angle ZXY$

$\angle MLK=\angle XYZ$