If a line is parallel to the base of a trapazium and bisects one of the non-parallel sides, then prove that it bisects either diagonal of the trapazium.
Asked by | 31st Oct, 2013, 05:03: PM
Given: ABCD is a trapezium. EF is parallel to DC. and it bisects one of the non parallel sides.
TPT: EF bisects either of the diagonals of the trapezium
let EF bisects AD, i.e. E is the mid-point of AD.
now in the triangle ADC,
E is the mid-point of AD and EM || DC (as EF is parallel to DC)
From the converse of the mid point theorem: the straight line drawn through the mid-point of one side of a triangle parallel to another , bisects the third side.
Therefore M is the mid point of AC.
Thus if EF bisects AD at E , it also bisects the diagonal AC.
Similarly we can show that if EF bisects BD at F , it also bisects the diagonal BD.
Answered by | 31st Oct, 2013, 10:40: PM
Kindly Sign up for a personalised experience
- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions
Verify mobile number
Enter the OTP sent to your number