Question

Match the similarity criteria for which $\Delta ABC\sim \Delta ADE$ in each case.

• A. AA similarity
• B. SAS similarity
• C. SSS similarity

Answer 1

Given DE || BC
So, $\angle ADE=\angle ABC$ and $\angle AED=\angle ACB$
[Pair of corresponding angles]
$\therefore$ $\Delta ABC\sim \Delta ADE$...(By AA similarity)


In the above figure $\angle EAD=\angle BAC$ [Vertically opposite angles are equal]
and $\frac{AD}{AB}=\frac{AE}{AC}=2$
This shows that sides are in proportion.
$\therefore$ From SAS criteria we can say $\Delta ABC\sim \Delta ADE$


In the above figure,
$\frac{AD}{AB}=\frac{AE}{AC}=\frac{DE}{BC}$
$⟹\frac{10}{2.5}=\frac{14}{3.5}=\frac{18}{4.5}=4$
$\therefore$ From SSS criteria we can say $\Delta ABC\sim \Delta ADE$