web analytics

Example 10 - ACB = 90 and CD perpendicular AB. Prove BC2/AC2 - Examples

  1. Class 10
  2. Important Questions for Exam - Class 10
Ask Download

Transcript

Example 10 In figure, ∠ ACB = 90° and CD ⊥ AB. Prove that BC2/AC2=BD/AD Given:- ΔCAB, ∠ ACB = 90° And CD ⊥ AB To Prove :- BC2/AC2=BD/AD Proof : From theorem 6.7, If a perpendicular is drawn from the vertex of the right angle to the hypotenuse then triangles on both sides of the Perpendicular are similar to the whole triangle and to each other So, ∆ 𝐴𝐶𝐷 ~ ∆ 𝐴𝐵𝐶 & ∆ 𝐵𝐶𝐷 ~ ∆ 𝐵𝐴𝐶. From (1) ∆ 𝐴𝐶𝐷 ~ ∆ 𝐴𝐵𝐶 If two triangles are similar , then the ratio of their corresponding sides are equal 𝐴𝐶/𝐴𝐵=𝐴𝐷/𝐴𝐶 AC ×𝐴𝐶=𝐴𝐵×𝐴𝐷 AC2 = AB ×𝐴𝐷 Similarly, from (2) ∆ 𝐵𝐶𝐷 ~ ∆ 𝐵𝐴𝐶 If two triangles are similar , then the ratio of their corresponding sides are equal 𝐵𝐶/𝐵𝐴=𝐵𝐷/𝐵𝐶 BC × BC = BA × BD BC2 = BA × BD Divide equation ((4))/((3)) 𝐵𝐶2/𝐴𝐶2=(𝐵𝐴 × 𝐵𝐷)/(𝐴𝐵 × 𝐴𝐷) 𝐵𝐶2/𝐴𝐶2=𝐵𝐷/𝐴𝐷 Hence proved

About the Author

CA Maninder Singh's photo - Expert in Practical Accounts, Taxation and Efiling
CA Maninder Singh
CA Maninder Singh is a Chartered Accountant for the past 8 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .
Jail