Question

We only need to check if the corresponding angles are equal for two triangles to be similar.

• A. True
• B. False

Answer 1

The correct option is A True


Take two triangles ABC and DEF such that
$\angle A=\angle D,\angle B=\angle Eand\angle C=\angle F$
Cut DP = AB and DQ = AC and join PQ.
So, $\Delta ABC\cong \Delta DPQ$ (SAS congruence)
This gives $\angle B=\angle P=\angle E$ and PQ || EF.
Therefore, $\frac{DP}{PE}=\frac{DQ}{QF}\Rightarrow \frac{PE}{DP}=\frac{QF}{DQ}\Rightarrow \frac{PE}{DP}+1=\frac{QF}{DQ}+1\Rightarrow \frac{DP+PE}{DP}=\frac{DQ+QF}{DQ}\Rightarrow \frac{DE}{DP}=\frac{DF}{DQ}$
DP = AB and DQ = AC,
$\Rightarrow \frac{DE}{AB}=\frac{DF}{AC}$
$\frac{AB}{DE}=\frac{AC}{DF}$
Similarly, $\frac{AB}{DE}=\frac{BC}{EF}$ and so $\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}$
Hence, if corresponding angles are equal in two triangles, they are similar as the ratio of corresponding sides is the same.