Last updated at May 29, 2018 by Teachoo

Transcript

Ex 6.2, 10 The diagonals of a quadrilateral ABCD intersect each other at the point O such that π΄π/π΅π = πΆπ/π·π . Show that ABCD is a trapezium Given: ABCD is a quadrilateral where diagonals AC & BD intersect at O & π΄π/π΅π=πΆπ/π·π To prove: ABCD is a trapezium Construction: Let us draw a line EF II AB passing through point O. Proof: Given π΄π/π΅π=πΆπ/π·π β π΄π/πΆπ=π΅π/π·π Now, in β π΄π·π΅ EO II AB π΄πΈ/π·πΈ=π΅π/π·π β π΄πΈ/π·πΈ=π΄π/πΆπ Thus in Ξ ADC, Line EO divides the triangle in the same ratio β΄ EO II DC Now, EO II DC But, we know that EO II AB β EO II AB II DC β AB II DC Hence, one pair of opposite sides of quadrilateral ABCD are parallel Therefore ABCD is a trapezium . 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 10 years. He provides courses for Maths and Science at Teachoo.