Question

Construct a triangle ABC with degree A = 60degree = angle B and AB=6c .measure the sides BC and CA

Answer 1

Steps to construct the triangle

Draw a line segment BC=6 cm

At B, draw ∠CBE=60o

Draw BF⊥BE

Draw the perpendicular bisector of BC intersecting BF at O.

With O as centre and radius equal to OB or OC draw a circle.

With D as centre and radius 5 cm, mark a point A on the circle.

Join AB and AC. This gives △ABC

With B as centre and radius 8 cm, mark an arc which intersect BC produced in C'.

Draw a line parallel to AC at C'.

Extend the line segment BA, which intersect the line passing through C' in A'.

Thus, △A BCis the required triangle.

Here, △A′BC′∼△ABC [AA similarity]