Question

Construct an isosceles triangle whose base is 9 cm and altitude 5cm. Construct another triangle whose sides are 3/4 of the corresponding sides of the first isosceles triangle.

Answer 1

Steps of Construction:

Step 1: Draw a line segment BC = 9cm

Step 2: With B as center, draw an arc each above and below BC.

Step 3: With C as center, draw an arc each above and below BC

Step 4: Join their points of intersection to obtain the perpendicular bisector of BC. Let it intersect BC at D

Step 5: From D, cut an arc of radius 5 cm and mark the point as A

Step 6: Join AB and AC

Thus △ABC is obtained

Step 5: Below BC. make an acute ∠CBX.

Step 6: Along BX, mark off four points B₁,B₂,B₃,B₄ such that

BB₁ = B₁B₂ = B₂B₃ = B₃B₄

Step 7: Join B₄C.

Step 8: From B₃. draw B₂E || B₄C meeting BC at E.

Step 9: From E. draw EF || CA meeting AB al F.

Thus, △FBE is the required triangle, each of whose sides is \(\frac{3}{4}\)the corresponding sides of the first triangle.