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

$\text{Take two triangles ABC and DEF such that}\angle A=\angle D,\angle B=\angle Eand\angle C=\angle F.\text{Cut DP = AB and DQ = AC and join PQ.}So,\Delta ABC\cong \Delta DPQ\text{(SAS congruence)}Thisgives\angle B=\angle P=\angle EandPQ\parallel EFTherefore,\frac{DP}{PE}=\frac{DQ}{QF}\Rightarrow \frac{PE}{DP}=\frac{QF}{DQ}\Rightarrow \frac{PE}{DP}+1=\frac{QF}{DQ}+1\Rightarrow \frac{DP+PE}{DP}=\frac{DQ+QF}{DQ}\Rightarrow \frac{DE}{DP}=\frac{DF}{DQ}$
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.