Question

Construct an isosceles triangle whose base is 9 cm and altitude 5 cm. Construct another triangle whose sides are $\frac{3}{4}$ 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, △ABC is obtained .
Step 5. Below BC, make an acute $\angle CBX$.
Step 6. Along BX, mark off four points B₁, B₂, B₃, B₄, such that BB₁=B₁B₂ = B₂B₃ = B₃B_4.
Step 7. Join B₄C.
Step 8. From B₃, draw B₃E ∥ B₄C, meeting BC at E.
Step 9. From E, draw EF ∥ CA, meeting AB at F.


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