Question 2 - Figure it out - Page 107 - Chapter 4 Class 8 - Quadrilaterals (Ganita Prakash)

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Question 2 Construct a kite whose diagonals are of lengths 6 cm and 8 cm.Since diagonals are given, we make diagram such that diagonal is horizontal For Kite ABCD Diagonal AC bisects diagonal BD ∴ OB = OD = 6/2 cm = 3 cm Also, diagonals are perpendicular to each other ∴ AC ⊥ BD So, ∠ DOA = ∠ BOA = ∠ DOC = ∠ BOC = 90° Let’s construct it Steps of construction Draw diagonal AC of length 8 cm Mark point O anywhere in the line AC, let’s mark it at 3 cm from point A 3. Since ∠ AOD = 90°. We make 90° angle from point O 4. Similarly, we make 90° on bottom of 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 kite