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## Construct a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then construct another triangle whose sides are 3 / 4 times the corresponding sides of the triangle ABC. Mathematics CBSE class 10 2017

Construct a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then construct another triangle whose sides are 3 / 4 times the corresponding sides of the triangle ABC.

By:tarun101

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## Answers

Sum of all side of triangle = 180°

∴ ∠A + ∠B + ∠C = 180°

∠C = 180° - 150° = 30°

Steps of Construction:

Step I: BC = 7 cm is drawn.

Step II: At B, a ray is drawn making an angle of 45° with BC.

Justification:

∠B = 45° (Common)

∠C = ∠C'

ΔAB'C' ~ ΔABC by AA similarity condition.

∴ BC/BC' = AB/A'B' = AC/A'C'

also,

BC/BC' = BB3/BB4 = 34

⇒ AB = 4/3 AB', BC = 4/3 BC' and AC = 4/3 A'C'

prajwalamv

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