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

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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