Question

Construct an equilateral triangle LMN, one of whose side is 5 cm. Bisect ∠ M of the triangle.

Answer 1

Construction Procedure:

1. Draw a line segment LM = 5 cm.
2. Taking L as centre and radius 5 cm draw an arc.
3. Taking M as centre and radius draw another arc intersecting previous arc at N.
4. Join LN and MN. Thus, ΔLMN is the required equilateral triangle.
5. Taking M as centre and any suitable radius, draw an arc intersecting LM at P and MN at Q.
6. Taking P and Q as centres and same radii, draw arcs intersecting at S.
7. Join MS and produce it meet LN at R. Thus, MSR is required bisector of ∠M.