Question 2 - Figure it out - Page 102 - Chapter 4 Class 8 - Quadrilaterals (Ganita Prakash)

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Question 2 Using the diagonal properties, construct a parallelogram whose diagonals are of lengths 7 cm and 5 cm, and intersect at an angle of 140°.Since diagonals are given, we make diagram such that diagonal is horizontal In parallelogram Diagonals bisect each other ∴ OA = OC = 7/2 cm = 3.5 cm ∴ OD = OC = 6/2 cm = 3 cm Also, given that diagonals intersect at an angle 140° ∴ ∠ AOD = 140° Let’s construct it Steps of construction Draw diagonal AC of length 7 cm Mark point O, such that AO = 3.5 cm 3. Since ∠ AOD = 90°. We make 90° angle from point O 4. We extend the same line below AC 5. Since OD = 3 cm, we open compass 3 cm And keeping pointy end O, we draw an arc to the line perpendicular from point O Where it intersects is point D 6. Since OB = 3 cm, we open compass 3 cm And keeping pointy end O, we draw an arc to the line perpendicular from point O below AC Where it intersects is point B 7. Join AB, BC, CD, AD and BD ∴ ABCD is the required parallelogram