Diagonals of a trapezium divide each other proportionally , Mathematics

Diagonals of a trapezium divide each other proportionally:

922_trapezium.png

Given : In trapezium ABCD , AB// DC
R.T.P :AO/OC = BO/OD

Construction: Draw the line PQ; parallel to AB or CD through O
Proof : In ΔACD, OP// CD

 AP/PD = AO/OC................... (1)

(Basic proportionality theorem)

In ΔABD, OP// AB

AP/PD = BO/OD.................(2)

(Basic proportionality theorem)

From (1) and (2) we have

AO/OC = BO/OD

i.e, The diagonals AC, BD divide each other proportionally.

 

 

Posted Date: 9/3/2012 4:37:56 AM | Location : United States







Related Discussions:- Diagonals of a trapezium divide each other proportionally , Assignment Help, Ask Question on Diagonals of a trapezium divide each other proportionally , Get Answer, Expert's Help, Diagonals of a trapezium divide each other proportionally Discussions

Write discussion on Diagonals of a trapezium divide each other proportionally
Your posts are moderated
Related Questions
The exponential functions are useful for describing compound interest and growth. The exponential function is defined as:          y = m. a x where '

ABC is a right-angled isosceles triangle, right-angled at B. AP, the bisector of ∠BAC, intersects BC at P. Prove that AC 2 = AP 2 + 2(1+√2)BP 2 Ans:    AC = √2AB (Sinc

Describe Multiplication and Division Equations? Multiplication Equations :  To solve multiplication equations, divide both sides of the equation by the number being multiplie

Determine all possible solutions to the subsequent IVP. y' = y ? y(0) = 0 Solution : First, see that this differential equation does NOT satisfy the conditions of the th

Scalar Equation of Plane A little more helpful form of the equations is as follows. Begin with the first form of the vector equation and write a vector for the difference. {

Eliment t from following equations v=u+at s=ut+1/2at^2

Here we look at only the rules without going into their proofs. They are: a  0. If a If a If a

Regression line drawn as y=c+1075x, when x was 2, and y was 239, given that y intercept was 11. Caculate the residual

Q. How to divide two fractions?If you want to divide two fractions, You invert the second fraction (that means, turn it upside-down) and multiply (change the division to a