Question

Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a triangle whose sides are 43 times the corresponding sides of ∆ABC.

Answer 1

Constructing ∆ABC

Step 1: Draw BC base of length .

Step 2: Draw a ray at an angle of 45° with line BC from point B .

Step 3: Draw a ray at an angle of 30° from line CB from Cpoint and mark the intersection point of the rays from and as .

Step 4: Join A-B and A-C .

∆ABC is the required triangle.

For constructing∆EBD~∆ABC

Step 1: Draw a ray BX at an acute angle to line BC on the opposite side of A .

Step 2: Mark 4 equidistant points

B1,B2,B3,B4 on ray BX.

Step 3: Join B3 and C .

Step 4: Draw B4B parallel to B4C and label the intersection on the extension of BC as D .

Step 5: Draw parallel DE to BA and label the intersection with the extension of BA as E.

∆EBDis the required triangle