List of top Mathematics Questions on Triangles asked in UP Board X

BL and CM are medians of a triangle ABC, right-angled at A. Prove that \( 4(BL^2 + CM^2) = 5BC^2 \).
If \( \triangle ABC \) is an equilateral triangle such that \( AD \perp BC \), then \( AD^2 \) is equal to:
ABC and BDE are two equilateral triangles such that D is the midpoint of BC. The ratio of the areas of the triangles ABC and BDE is:
If one side of an isosceles right triangle is \( 5\sqrt{2} \) cm, then the length of its hypotenuse is:
If a line intersects sides \( AB \) and \( AC \) of a triangle \( ABC \) at \( D \) and \( E \) respectively and is parallel to \( BC \), prove that \( \frac{AD}{AB} = \frac{AE}{AC} \).
If \( \triangle ABC \) is an equilateral triangle of side \( 2a \), the length of each of its altitudes will be:
The ratio of the areas of two triangles is equal to the square of the ratio of their corresponding sides. Then these triangles will be:
If \( \triangle ABC \) is an isosceles triangle with \( AB = AC \), then:
In $\triangle ABC$, if $AB = 6\sqrt{3}$ cm, $AC = 12$ cm, and $BC = 6$ cm, then $\angle B$ will be: