Question

In the figure given above, L is any point on the bisector of the acute angle $ABC$ and the line $ML$ is parallel to $BC$. Which one of the following is correct?

• A. The triangle $BML$ is equilateral
• B. The triangle $BML$ is isosceles but right-angled
• C. The triangle $BML$ is isosceles but not right-angled
• D. The triangle $BML$ is not isosceles

Answer 1

The correct option is C The triangle $BML$ is isosceles but not right-angled

R.E.F image

Given $:L$ is any point on bisector

of acute angle $ABC$

$ML\parallel BC$

Therefore, BL is bisector of $\angle ABC$

(bisector is any line segment which

divides into equal half)

Therefore, $\angle ABL=\angle LBC=m$ (say)

Given that $ML\parallel BC$

Therefore, $\angle MLB=\angle LBC$ (alternate angle theorem)

Therefore, $\Delta BML$ is an isosceles triangle

But $\angle BML$ may not be ${90}^o$

Therefore, $\Delta BML$ is not right angled triangle

Hence, $\Delta BML$ is isosceles but not right angled