Question : In $\triangle ABC$, AB = BC = $k$, AC =$\sqrt2k$, then $\triangle ABC$ is a:

Option 1: Isosceles triangle

Option 2: Right-angled triangle

Option 3: Equilateral triangle

Option 4: Right isosceles triangle

Question : ABC is an isosceles right-angled triangle with $\angle$B = 90°. On the sides AC and AB, two equilateral triangles ACD and ABE have been constructed. The ratio of the area of $\triangle$ABE and $\triangle$ACD is:

Option 1: $1 : 3$

Option 2: $2 : 3$

Option 3: $1 : 2$

Option 4: $1 : \sqrt{2}$

Question : If the three medians of a triangle are the same then the triangle is:

Option 1: equilateral

Option 2: isosceles

Option 3: right angled

Option 4: obtuse angle

Question : In $\triangle$ABC, D and E are two points on the sides AB and AC, respectively, so that DE $\parallel$ BC and $\frac{AD}{BD}=\frac{2}{3}$. Then $\frac{\text{Area of trapezium DECB}}{\text{Area of $\triangle$ABC}}$ is equal to:

Option 1: $\frac{5}{9}$

Option 2: $\frac{21}{25}$

Option 3: $1\frac{4}{5}$

Option 4: $5\frac{1}{4}$

Question : $\triangle ABC$ is an isosceles triangle with AB = AC. If $\angle BAC=50^\circ$, then the degree measure of $\angle ABC$ is equal to:

Option 1: $70^\circ$

Option 2: $55^\circ$

Option 3: $60^\circ$

Option 4: $65^\circ$