Question

Using which of the following measurements, can a $△$ ABC be constructed ?

• A. $\angle A={75}^{\circ },\angle B={60}^{\circ },BC=5cm$
• B. $AB=5cm,BC=6cm,\angle ABC={60}^{\circ }$
• C. AB = 4 cm, BC = 6cm, CA = 2 cm
• D. $AB=5cm,BC=6cm,\angle ACB={60}^{\circ }$

Answer 1

Answer: (A), (B)

The correct options are
A

$\angle A={75}^{\circ },\angle B={60}^{\circ },BC=5cm$

B

$AB=5cm,BC=6cm,\angle ABC={60}^{\circ }$

Using Option A - a triangle can be constructed as two angles and one side are given.

Using Option B - a triangle can be constructed as two sides and an included angle is given.

Using Option C - a triangle cannot be constructed because the sum of two sides (AB and CA) is not greater than the third side BC.

Using Option D - a triangle cannot be constructed as the angle given is not the included angle.