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Ex 8.2, 7 - ABC is a triangle right angled at C. A line - Ex 8.2

  1. Chapter 8 Class 9 Quadrilaterals
  2. Serial order wise
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Ex 8.2, 7 ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that D is the mid-point of AC Given: ∆ ABC is right angled triangle, ∠ C = 90° M is the mid-point of AB, MD ∥ BC To prove: D is mid-point of AC, i.e., AD = CD Proof: In ΔABC, M is the mid-point of AB and MD ∥ BC. ∴ D is the mid-point of AC. Ex 8.2, 7 ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that (ii) MD ⊥ AC As MD ∥ BC & AC is transversal ∴ ∠MDC + ∠BCD = 180° ∠MDC + 90° = 180° ∠MDC = 90° ∴ MD ⊥ AC Hence proved Ex 8.2, 7 ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that (iii) CM = MA = 1/2 AB Join MC. In ΔAMD and ΔCMD, AD = CD ∠ADM = ∠CDM DM = DM ∴ ΔAMD ≅ ΔCMD ∴ AM = CM However, AM =  1/2 AB From (1) & (2) ⇒ CM = AM = 1/2 AB

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