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Mathematics

In the adjoining figure, ABCD is a quadrilateral in which BN and DM are drawn perpendiculars to AC such that BN = DM. If OB = 4 cm, then BD is

  1. 6 cm

  2. 8 cm

  3. 10 cm

  4. 12 cm

In the adjoining figure, ABCD is a quadrilateral in which BN and DM are drawn perpendiculars to AC such that BN = DM. If OB = 4 cm, then BD is? Triangles, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Triangles

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Answer

∠MOD = ∠NOB (Vertically opposite angles)

∠DMO = ∠BNO (Each = 90°)

BN = DM (Given)

Hence, △MOD ≅ △NOB by AAS axiom.

We know that corresponding parts of congruent triangles are equal.

OD = OB = 4 cm.

BD = OB + OD = 4 + 4 = 8 cm.

Hence, Option 2 is the correct option.

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