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Example 2 - Show that diagonals of rhombus are perpendicular - Examples

  1. Chapter 8 Class 9 Quadrilaterals
  2. Serial order wise
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Example 2 Show that the diagonals of a rhombus are perpendicular to each other. Given: Rhombus ABCD To prove : AC ⊥ BD Proof: Since ABCD is a rhombus ∴ AB = BC = CD = DA In Δ AOB and Δ COB, OA = OC OB = OB AB = CB ∴ Δ AOB ≅ Δ COB ⇒ ∠ AOB = ∠ COB Since AC is a line, ∠ AOB + ∠ COB = 180° ∠ AOB + ∠ AOB = 180° 2∠ AOB = 180° ∠ AOB = 180"°" /2 = 90° From (1) ∠ COB = ∠ AOB ∠ COB = 90° Also, ∠ DOC = ∠ AOB = 90° ∠ AOD = ∠ COB = 90° Since ∠ DOC = ∠ AOB = ∠ AOD = ∠ COB = 90° ⇒ AC ⊥ BD ∴ The diagonals of a rhombus are perpendicular to each other.

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