Question

Construct a triangle ABC in which BC = 5 cm, ZB = 60° and
5
AB + AC = 8 cm. Then construct a triangle whose sides are of the
4
corresponding sides of AABC.
E​

Answer 1

Answer:

Steps of construction

1.  Draw a line segment AB=4 cm.

2.  Construct ∠ABP=60.

3.  Draw a line GH∥AB at a distance of 3cm, intersecting BP at C.

4.  Join CA. Thus, △ABC is obtained.

5.  Extend AB to D such that AD=23AB=(23×4)cm=6 cm.

6.  Draw DE∥BC, cutting AC produced at E. Then, △ADE is the required triangle similar to △ABC such that each side of △ADE is 23times the corresponding side of △ABC.

Proof: Since DE∥BC, we have : △ADE∼△ABC

∴ABAD=BCDE=ACAE=23.