Question

A triangle ABC in which BC = 3.4 cm, AB - AC = 1.5 cm and DB = 45${}^{\circ }$ can be constructed using compass and ruler.

• A. True
• B. False

Answer 1

The correct option is A True

A triangle in which the difference of two sides is less than the third side can be made. The steps are as follows:

Step 1 : Draw a line segment BC of length 3.4cm.

Step 2 : Draw an angle of 45$\circ$ from point B.

Step 3 : From Ray BX cut off the line segment BD = 1.5cm.

Step 4 : Join D to C.

Step 5 : Draw bisector of DC.

Step 6 : Extend bisector of DC to intersect the Ray BX at point A.

Step 7 : Join A to C, $\Delta$ ABC is the required triangle.