Question

Construct $△$GHI such that GI = 5.4 cm , $\angle$GHI = 75$°$ and Median HR = 3.2 cm.

Answer 1

Steps of construction:
(i) Draw a line segment GI = 5.4 cm.
(ii) Through G, draw GX such that $\angle$IGX = 75$°$
(iii) Draw GY$\perp$GX.
(iv) Draw the perpendicular bisector of GI intersecting GY at O and GI at R.
(v) With O as the centre and OG as the radius, draw a circle.
(vi) The major arc GWI of the circle contains the vertical 75$°$.
(vii) With R as the centre, draw an arc of radius 3.2 cm meeting the circle at H and H'.
Thus, $△$GHI or $△$GH'I is the required triangle.