Question

Given that AB = 4cm and BC = 6.5cm , which of the following information is required to construct $△ABC$?

• A. $\angle ACB$ = ${60}^{\circ }$
• B. $\angle ABC$ = ${60}^{\circ }$
• C. AD = 3 cm
• D. None of the above

Answer 1

The correct option is B $\angle ABC$ = ${60}^{\circ }$

To construct a triangle with two known sides, the included angle also has to be known. The included angle here is $\angle ABC$ = ${60}^{\circ }$
Steps involved to construct a triangle, given two sides and an included angle is as follows:

• Draw a rough sketch of the triangle.
• Draw BC = 6.5cm.
• With the help of compass, construct $\angle PBC={60}^{\circ }$.
• With B as centre, draw an arc of 4cm length which cuts BP at point A.
  $\therefore$ BA = 4 cm.
• Join A and C.