Question

Construct a ΔABC with base BC = 3.5 cm, vertical angle ∠ BAC = 45°, and median through the vertex A is 3.5 cm. Write also the steps of construction.

Answer 1

Steps of construction:
1) Draw a line segment BC = 3 cm and make ∠ CBP = 45°
2) Construct EB ⊥ BP.
3) Draw the perpendicular bisector of BC its intersecting BE in O and BC in D.
4) Draw a circle taking O as a centre and OB as the radius.
5) Now with D as centre and radius = 3.5 cm. draw arcs of the circle intersecting the above-drawn circle in A and A'.
6) Join AB, AC and A'B, A'C.
Then the Δs, ΔABC and ΔA'BC are the required triangles.