Question

Which of these triangles can be constructed?

• A. $△\mathrm{ABC},\mathrm{AB}=5\mathrm{cm},\angle A=85°,\angle B=115°$
• B. $\Delta \mathrm{PQR},\mathrm{QR}=4.7\mathrm{cm},\angle Q=30°,\angle R=60°$
• C. $△\mathrm{ABC},\mathrm{BC}=4\mathrm{cm},\mathrm{AB}=3\mathrm{cm},\angle C=90°$
• D. $△\mathrm{LMN},\mathrm{LM}=5\mathrm{cm},\angle L=60°,\angle N=120°$

Answer 1

The correct option is B $\Delta \mathrm{PQR},\mathrm{QR}=4.7\mathrm{cm},\angle Q=30°,\angle R=60°$

$△\mathrm{PQT},\mathrm{QR}=4.7\mathrm{cm},\angle Q=30°,\angle R=60°$According to ASA criteria, if we get two angles and included side, we can construct the triangle. Option A and D does not satisfy Angle Sum Property. In option C, AB = 3cm and BC = 4 cm but according to Pythagorus $AB>BC$ ($\angle C={90}^o$). $A{B}^2=B{C}^2+A{C}^2$