Question : ABC is an isosceles triangle such that AB = AC, $\angle$ABC = 55°, and AD is the median to the base BC. Find the measure of $\angle$BAD.

Option 1: 50°

Option 2: 55°

Option 3: 35°

Option 4: 90°

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°

Question : In $\triangle$ABC, $\angle$B = 35°, $\angle$C = 65° and the bisector of $\angle$BAC meets BC in D. Then $\angle$ADB is:

Option 1: 40°

Option 2: 75°

Option 3: 90°

Option 4: 105°

Question : ΔABC and ΔDEF are congruent respectively. If AB = 6 = DE, BC = 8 = EF and $\angle$B = 30°, then $\angle$D + $\angle$C _________.

Option 1: 160°

Option 2: 120°

Option 3: 130°

Option 4: 150°

Question : In triangle ABC, $\angle$ B = 90°, and $\angle$C = 45°. If AC = $2 \sqrt{2}$ cm then the length of BC is:

Option 1: 3 cm

Option 2: 2 cm

Option 3: 1 cm

Option 4: 4 cm