Question : In an isosceles $\triangle ABC$, AD is the median to the unequal side BC meeting at D, DP is the angle bisector of $\angle ADB$ and PQ is drawn parallel to BC meeting AC at Q. Then, the measure of $\angle PDQ$ is:

Option 1: 130°

Option 2: 90°

Option 3: 180°

Option 4: 45°

Question : In an isosceles $\triangle ABC$, $AB = AC$, $XY || BC$. If $\angle A=30°$, then $\angle BXY$?

Option 1: 75°

Option 2: 30°

Option 3: 150°

Option 4: 105°

Question : The vertical angle $\angle A$ of an isosceles $\triangle ABC$ is three times the angle B on it. The measure of the $\angle A$ is:

Option 1: 90°

Option 2: 108°

Option 3: 100°

Option 4: 36°

Question : ABC is a right angle triangle and $\angle ABC = 90^{\circ}$. BD is perpendicular on the side AC. What is the value of $(BD)^2$?

Option 1: $AD\times DC$

Option 2: $BC\times AB$

Option 3: $BC\times CD$

Option 4: $AD\times AC$

Question : In $\triangle$ABC, AB = $a - b$, AC = $\sqrt{a^2+b^2}$, and BC = $\sqrt{2ab}$, then find angle B.

Option 1: 60°

Option 2: 30°

Option 3: 90°

Option 4: 45°