Last updated at May 29, 2018 by Teachoo

Transcript

Example 1 If a line intersects sides AB and AC of a Ξ ABC at D and E respectively and is parallel to BC, prove that π΄π·/π΄π΅=π΄πΈ/π΄πΆ Given: Ξ ABC , where line intersects sides AB and AC at D and E. And DE II BC To Prove : π΄π·/π΄π΅=π΄πΈ/π΄πΆ Proof: We know that if a line drawn parallel to one side of triangle, intersects the other two sides in distinct points, then it divides the other 2 side in same ratio Therefore , π΄π·/π·π΅=π΄πΈ/πΈπΆ π΄π·/π·π΅=π΄πΈ/πΈπΆ π·π΅/π΄π· =πΈπΆ/π΄πΈ Adding 1 on both sides π·π΅/π΄π·+1=πΈπΆ/π΄πΈ+1 (π·π΅ + π΄π·)/π΄π· =(πΈπΆ + π΄πΈ)/π΄πΈ π΄π΅/π΄π·=π΄πΆ/π΄πΈ π΄π·/π΄π΅=π΄πΈ/π΄πΆ Hence proved

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.