Answer :

To construct a ΔABC, we first need to find ∠C

We know that,

Sum of angles of a triangle = 180°

⇒ ∠A + ∠B + ∠C = 180°

⇒ 105° + 45° + ∠C = 180°

⇒ 150° + ∠C = 180°

⇒ ∠C = 30°

Now, we construct ΔABC

Steps of construction:

1. Draw base BC = 7cm

2. With the help of compass, draw an angle ∠B = 45°

3. With the help of compass, draw ∠C = 30°

4. Mark point A where two rays intersect

∴ ΔABC is the required triangle

Now, we need to make a triangle which is times its size

Steps of construction:

1. Draw any ray BX making an acute angle with BC on the side opposite to the vertex A

2. Mark 4 (the greater of 3 and 4 in ) points B_{1}, B_{2}, B_{3}, B_{4} on BX so that BB_{1} = B_{1}B_{2} = B_{2}B_{3} = B_{3}B_{4}

3. Join B_{4}C and draw a line through B_{3} (the 3^{rd} point, 3 being smaller of 3 and 4 in ) parallel to B_{4}C, to intersect BC at C’

4. Draw a line through C’ parallel to the line AC to intersect AB at A’

Thus, A’BC’ is the required triangle.

Rate this question :