Question 5 of 13intermediate🔧 ApplyDiagram3 marks

Using the diagonal properties, construct a parallelogram whose diagonals are of lengths 7 cm and 5 cm, and intersect at an angle of 140°.

Correct Answer

Draw two line segments of lengths 7 cm and 5 cm that bisect each other at an angle of 140°. The point of intersection divides each diagonal into two equal parts (3.5 cm and 2.5 cm respectively). Join the four endpoints to form the parallelogram.

Exercise: Figure it Out (Section 2) | Q: 2 | (Page Page 21)
For More Understanding

Explanation

Property 4 of parallelograms states that the diagonals bisect each other. To construct the parallelogram: (1) Draw diagonal AC = 7 cm with midpoint O. (2) From O, draw diagonal BD = 5 cm at 140° to AC. (3) Mark points such that OA = OC = 3.5 cm and OB = OD = 2.5 cm. (4) Join A, B, C, D to form the parallelogram.

Solution Steps

  1. Step 1: Draw a line segment AC = 7 cm and mark its midpoint O.

  2. Step 2: At point O, draw another line segment BD = 5 cm at an angle of 140° to AC.

  3. Step 3: Ensure O is the midpoint of BD (OB = OD = 2.5 cm).

  4. Step 4: Join points A, B, C, D in order to form the parallelogram ABCD.

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