Last updated at May 29, 2018 by Teachoo

Transcript

Example 2 ABCD is a trapezium with AB || DC. E and F are points on non-parallel sides AD and BC respectively such that EF is parallel to AB (see Fig. 6.14). Show that π΄πΈ/πΈπ· = π΅πΉ/πΉπΆ Given: ABCD is a trapezium where AB II DC E and F are points non parallel sides AD and BC such that EF II AB To Prove: π΄πΈ/πΈπ·=π΅πΉ/πΉπΆ Proof: Given AB II DC & EF II AD So, EF II DC Joining A & C Let AC intersect EF at point G Now in β π΄π·πΆ EG II DC So, π΄πΈ/πΈπ·=π΄πΊ/πΊπΆ Similarly , in β πΆπ΄π΅ AB II GF So, π΄πΊ/πΊπΆ=π΅πΉ/πΉπΆ From (1) and (2) π΄πΈ/πΈπ·=π΄πΊ/πΊπΆ=π΅πΉ/πΉπΆ π΄πΈ/πΈπ·=π΅πΉ/πΉπΆ 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.