Question

By using ruler and compass only, construct a quadrilateral ABCD in which AB = 6.5 cm, AD = 2 cm and ∠DAB = 75°. C is equidistant from the sides AB and AD, also C is equidistant from the points A and B.

Answer 1

• Draw a line segment AB = 6.5 cm.
• At point A, construct an angle of 75°.
• On this angle, mark AD = 2 cm and locate point D.
• Draw the angle bisector of ∠DAB.
• Draw the perpendicular bisector of AB.
• The intersection of these two bisectors gives point C.
• Join C to D and C to B to complete quadrilateral ABCD.

Since point C lies on the angle bisector of ∠DAB, it is equidistant from the sides AB and AD. Since point C lies on the perpendicular bisector of AB, it is equidistant from the points A and B. Therefore, quadrilateral ABCD is correctly constructed according to the given conditions.