0

Guest

Courses New

if abcd is a quadrilateral and e & f are midpoint of ac & bd respectively. prove that ab+ac+cb+cd = 4ef

if abcd is a quadrilateral and e & f are midpoint of ac & bd respectively. prove that ab+ac+cb+cd = 4ef

Grade:12th pass

1 Answers

Satyajit Samal
askIITians Faculty 34 Points
8 years ago
The correct question isAB+AD+CB+CD=4EF
Since F is the midpoint of BD, we getAB+AD = 2AF…...(1)
Similarly CB+CD = 2 CF…....(2)
Adding (1) and (2) we getAB+AD+CB+CD=2\left ( AF+CF \right ) \\ \Rightarrow AB+AD+CB+CD = -2\left ( FA+FC \right ) \\ \Rightarrow AB+AD+CB+CD = -2 \left ( 2FE \right ) \\ \RIghtarrow AB+AD+CB+CD = 4EF
Hence proved.

Think You Can Provide A Better Answer ?

Other Related Questions on Vectors

View all Questions »

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More