Question : In $\triangle$ABC and $\triangle$PQR, AB = PQ and $\angle$B = $\angle$Q. The two triangles are congruent by SAS criteria if:

Option 1: BC = QR

Option 2: AC = PR

Option 3: AC = QR

Option 4: BC = PQ

Question : ABC is an isosceles triangle having AB = AC and $\angle$A = 40$^\circ$. Bisector PO and OQ of the exterior angle $\angle$ ABD and $\angle$ ACE formed by producing BC on both sides, meet at O, then the value of $\angle$BOC is:

Option 1: 70$^\circ$

Option 2: 110$^\circ$

Option 3: 80$^\circ$

Option 4: 55$^\circ$

Question : If it is given that for two right-angled triangles $\triangle$ABC and $\triangle$DFE, $\angle$A = 25°, $\angle$E = 25°, $\angle$B = $\angle$F = 90°, and AC = ED, then which one of the following is TRUE?

Option 1: $\triangle \mathrm{ABC} \cong \triangle \mathrm{FED}$

Option 2: $\triangle \mathrm{ABC} \cong \triangle \mathrm{DFE}$

Option 3: $\triangle \mathrm{ABC} \cong \triangle \mathrm{EFD}$

Option 4: $\triangle \mathrm{ABC} \cong \triangle \mathrm{DEF}$

Question : I is the incenter of a triangle ABC. If $\angle$ ABC = 65$^\circ$ and $\angle$ ACB = 55$^\circ$, then the value of $\angle$ BIC is: 

Option 1: 130$^\circ$

Option 2: 120$^\circ$

Option 3: 140$^\circ$

Option 4: 110$^\circ$

Question : If in $\triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}, \frac{A B}{D E}=\frac{B C}{F D}$, then they will be similar when:

Option 1: $\angle B=\angle D$

Option 2: $\angle A=\angle D$

Option 3: $\angle A=\angle F$

Option 4: $\angle B=\angle E$