Question

Draw a right triangle ABC in which $BC=12\text{cm}$ cm, $AB=5\text{cm}$ cm and $\angle B={90}^{\circ }.$ Construct a triangle similar to it and of scale factor $\frac{2}{3}$. Is the new triangle also a right triangle?

• A. Yes
• B. No
• C. Can't say
• D. Data insufficient

Answer 1

The correct option is A Yes

In $△ABC$,

$AB=5\text{cm}$, $BC=12\text{cm}$, $\angle B={90}^{\circ }$

To construct-

A $△$ of scale factor $\frac{2}{3}$ which is similar to $△ABC$ as well.

Construction:-

• $BC$ is divided into ratio $2:3$ at $D$.
• $DE$ drawn parallel to $AB$.
• It intersects $AC$ at $E$.
• $△DEC$ is the desired $△$.

From the figure we can easily conclude that $△DEC$ is a right angle triangle as well.