Question

Draw an isosceles triangle ABC in which AB = AC = 6 cm and BC = 5 cm. Construct a triangle PQR similar to AABC in which PQ = 8 cm. Also justify the construction.

Answer 1

Steps of construction

1. Draw a line segment BC = 5 cm.

2. Construct OQ the perpendicular bisector of line segment BC meeting BC at P’.

3. Taking B and C as centres draw two arcs of equal radius 6 cm intersecting each other at A

4. Join BA and CA. So, ΔABC is the required isosceles triangle.

5. From B, draw any ray BX making an acute ∠CBX

6. Locate four points B₁, B₂, B₃ and B₄ on BX such that BB₁ = B₁B₂ = B₂B₃ = B₃B₄

7. Join B₃C and from B₄ draw a line B₄R || B₃C intersecting the extended line segment BC at R.

8. From point R, draw RP||CA meeting BA produced at P

Then, ΔPBR is the required triangle.