Construct a kite whose diagonals are of lengths 6 cm and 8 cm.
Draw two perpendicular line segments of lengths 6 cm and 8 cm. The longer diagonal (8 cm) should be the one that is bisected by the shorter diagonal. The shorter diagonal (6 cm) is bisected by the longer diagonal. Join the four endpoints to form the kite.
Explanation
Property 1 of kites states that one diagonal bisects the other at right angles. In a kite ABCD with AB = BC and CD = DA, diagonal BD bisects diagonal AC at right angles. To construct: (1) Draw diagonal AC = 8 cm with midpoint O. (2) Draw diagonal BD = 6 cm perpendicular to AC at O, but BD is not bisected—only AC is bisected. (3) The point where diagonals meet divides AC into two equal parts but not BD.
Solution Steps
Step 1: Draw the longer diagonal AC = 8 cm.
Step 2: Mark its midpoint O (so OA = OC = 4 cm).
Step 3: At point O, draw a perpendicular line segment BD = 6 cm.
Step 4: Note that O is NOT the midpoint of BD in a kite (only one diagonal bisects the other).
Step 5: Join points A, B, C, D to form the kite.