CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard
You are here
CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard
Last updated at Dec. 13, 2024 by Teachoo
The rest of the post is locked. Join Teachoo Black to see the full post.
Transcript
Question 26 (B) In 𝛥ABC, P and Q are points on AB and AC respectively such that PQ is parallel to BC. Prove that the median AD drawn from A on BC bisects PQ. We need to prove R is mid-point of PQ i.e. PR = RQ Since PQ ∥ BC And AB is transversal ∠ APR = ∠ ABD Similarly, PQ ∥ BC And AC is transversal ∠ AQR = ∠ ACD In Δ APR & Δ ABD ∠ PAR = ∠ BAD ∠ APR = ∠ ABD Δ APR ~ Δ ABD Since ratio of sides of similar triangle are equal 𝑨𝑷/𝑨𝑩=𝑷𝑹/𝑩𝑫 In Δ AQR & Δ ACD ∠ QAR = ∠ CAD ∠ AQR = ∠ ACD Δ AQR ~ Δ ACD Since ratio of sides of similar triangle are equal 𝑨𝑸/𝑨𝑪=𝑸𝑹/𝑪𝑫 Also, In Δ APQ & Δ ABC ∠ APQ = ∠ ABC ∠ AQP = ∠ ACB Δ APQ ~ Δ ABC Since ratio of sides of similar triangle are equal 𝑨𝑷/𝑨𝑩=𝑨𝑸/𝑨𝑪 And from (1) and (2) 𝑨𝑷/𝑨𝑩=𝑷𝑹/𝑩𝑫 & 𝑨𝑸/𝑨𝑪=𝑸𝑹/𝑪𝑫 From (1), (2) and (3) 𝑷𝑹/𝑩𝑫=𝑸𝑹/𝑪𝑫 Since BD = CD given 𝑃𝑅/𝐵𝐷=𝑄𝑅/𝐵𝐷 PR = QR Hence proved
