Diagonals of a trapezium divide each other proportionally , Mathematics

Assignment Help:

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.

 

 


Related Discussions:- Diagonals of a trapezium divide each other proportionally

What is the meaning of the f-statistic and f test, You are given the follow...

You are given the following regression results estimating the demand for widgets based on time series data for the past 40 months. Q t = 2.5 - 0.3 x P t + 12 x M t Where Q

Linear programming, function [x, z] = readSolution(tableau, basis)

function [x, z] = readSolution(tableau, basis)

Compute the probability of event, 1) Let the Sample Space S = {1, 2, 3, 4, ...

1) Let the Sample Space S = {1, 2, 3, 4, 5, 6, 7, 8}. Suppose each outcome is equally likely. Compute the probability of event E = "an even number is selected". P(E) = 2) A s

Polynomials in two variables, Polynomials in two variables Let's take a...

Polynomials in two variables Let's take a look at polynomials in two variables.  Polynomials in two variables are algebraic expressions containing terms in the form ax n y m

What is the average temperature on the celsius scale, Peggy's town has an a...

Peggy's town has an average temperature of 23° Fahrenheit in the winter. What is the average temperature on the Celsius scale? If the total amount for both is 80, after that th

Find and classify the differential equation, Find and classify the equilibr...

Find and classify the equilibrium solutions of the subsequent differential equation. y' = y 2 - y - 6 Solution The equilibrium solutions are to such differential equati

Adding & subtracting i guess, Jack and his mother paid $11.50 for tickets t...

Jack and his mother paid $11.50 for tickets to the movies, and adults tickets cost $4.50 more than a child ticket what was the cost of each ticket?

Calculate probability, The following table contains some information about...

The following table contains some information about the model used. Assume the probabilities given by the model are those of being a good writer. Variable

How long will it take him to plow 21 acres, Mr. Brown plowed 6 acres in 1 h...

Mr. Brown plowed 6 acres in 1 hour. At this rate, how long will it take him to plow 21 acres? Mr. Brown plows 6 acres an hour, so divide the number of acres (21) through 6 to f

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd