Question

Without using set square or protractor, construct rhombus ABCD with sides of length 4 cm and diagonal AC of length 5 cm. Measure ABC. Find the point R on AD such that RB = RC. Measure the length of AR.

Answer 1

Draw AB = 4 cm as the base of the rhombus.
From A draw an arc of radius 5 cm and from B an arc of radius 4 cm.

Their intersection gives point C. Then from C and A draw arcs of radius 4 cm; their intersection gives point D. Join A, B, C, and D to complete rhombus ABCD, and draw diagonal AC.

On measuring ∠ABC, we get 78°.

To locate point R such that RB = RC, we use the fact that a point equidistant from two points lies on the perpendicular bisector of the line segment joining them.

In the figure, PQ is the perpendicular bisector of BC and meets AD at R, giving AR = 1.2 cm.

Hence, ∠ABC = 78° and AR = 1.2 cm.