Question : In $\triangle$ABC, BD and CE are perpendicular to AC and AB respectively. If BD = CE, then $\triangle$ABC is:

Option 1: Equilateral

Option 2: Isosceles

Option 3: Right–angled

Option 4: Scalene

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 a $\triangle ABC$, the median AD, BE, and CF meet at G, then which of the following is true?

Option 1: 4(AD + BE + CF) > 3(AB + BC + AC)

Option 2: 2(AD + BE + CF) > (AB + BC + AC)

Option 3: 3(AD + BE + CF) > 4(AB + BC + AC)

Option 4: AB + BC + AC > AD + BE + CF

Question : $\triangle \mathrm{ABC}$ is an isosceles triangle with $\angle \mathrm{ABC}=90^{\circ}$ and $\mathrm{AB}=\mathrm{BC}$. If $\mathrm{AC}=12 \mathrm{~cm}$, then the length of $\mathrm{BC}$ (in $\mathrm{cm}$) is equal to:

Option 1: $6 \sqrt{2}$

Option 2: $8$

Option 3: $6$

Option 4: $8 \sqrt{2}$