Question 3 - Figure it out - Page 102 - Chapter 4 Class 8 - Quadrilaterals (Ganita Prakash)

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Question 3 Using the diagonal properties, construct a rhombus whose diagonals are of lengths 4 cm and 5 cm.Since diagonals are given, we make diagram such that diagonal is horizontal We know that In rhombus, Diagonals bisect each other at right angles ∴ OA = OC = 5/2 cm = 2.5 cm ∴ OD = OC = 4/2 cm = 2 cm And ∠ DOA = ∠ BOA = ∠ DOC = ∠ BOC = 90° Let’s construct it Steps of construction Draw diagonal AC of length 5 cm Mark point O, such that AO = 2.5 cm 3. Since ∠ AOD = 90°. We make 90° angle from point O 4. Similarly, we make 90° on bottom of AC 5. Since OD = 2 cm, we open compass 2 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 = 2 cm, we open compass 2 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 rhombus