Question

Construct an isosceles triangle whose base is 9 cm and altitude 5 cm. 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 = 9 cm.

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

Step 3: With C as centre, 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 ΔABC is obtained.

Step 7: Below BC. Make an acute ∠CBX.

Step 8: Along BX, mark of four points B₁, B₂, B₃, B₄ such that BB₁ = B₁B₂ = B₂B₃ = B₃B₄.

Step 9: Join B₄C.

Step 10: From B₃, draw B₂E || B₄C meeting BC at E.

Step 11: From E, draw EF || CA meeting AB at F.

Thus, ΔFBE is the required triangle, each of whose sides is `3/4` the corresponding sides of the first triangle.