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Example 8 - l, m and n are three parallel lines intersected - Mid point theorem

  1. Chapter 8 Class 9 Quadrilaterals
  2. Serial order wise
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Example 8 l, m and n are three parallel lines intersected by transversals p and q such that l, m and n cut off equal intercepts AB and BC on p . Show that l, m and n cut off equal intercepts DE and EF on q also. Given: l ∥ m ∥ n l, m and n cut off equal intercepts AB and BC on p So, AB = BC To prove: l, m and n cut off equal intercepts DE and EF on q i.e. DE = EF Proof: Let us join A to F intersecting m at G.. In Δ ACF, B is the mid-point of AC & BG ∥ CF So, G is the mid-point of AF In ∆ AFD, G is the mid-point of AF & GE ∥ AD So, E is the mid-point of DF Since E is the mid-point of DF, DE = EF Hence proved

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