geometry
posted by Anonymous .
A pentagon ABCDE. EG drawn parallel to DA meets BA produced at G and CF drawn parallel to DB meets AB produced at F. Prove that the area of pentagon ABCDE is equal to the area of triangle GDF.

Lets concentrate on the quadrilateral ADEG.
let the intersection of AE and DB be K
GE  AD (given)
So triangles ADE and ADG have the same base AD and the same height , since parallel lines are equal distances apart.
So triangle ADE = triangle ADG
but ADK is common to both, so subtracting ...
triangle AKG = triangle DEK
similarly by letting FD and BC intersect at L we can show that triangle FLB = triangle CDL
pentagon ABCDE
= triangle BLD + triangle LCD + triangle ABD + triangle DEK + triangle ADK
= triangle BLD + triangle FLB + triangle ABD + triangle GAK + triangle ADk
= triangle FDG 
tri FDG

In given figure X and Y are the mid point of AC and AB respectively QP parallel BC and CYQ and BXP are straight line. Prove that ar Triangle ABP =ar triangle ACQ

Since Y and X are the nid points of AB and AC ; by mid point theorem XY  BC. Now consider the ∆ BCQ and ∆ CBP their areas are equal cz they are on same base BC and between the same parallels
: AR(BCQ) = AR(BCP)
Let the intersection point of QC and BP be O
: add AR(AQOP) both sides.....
Therefore AR (ABP) =AR(ACQ) 
Jabbba jabba kappale mayathu

This question is wrong
Respond to this Question
Similar Questions

geometry
In the diagram, ABCDE is a regular pentagon with the measure of represented by 2x + 1. If the perimeter of the pentagon is 45, find the value of x. 
geometry
Find the area of a pentagon ABCDE with verticles A(0,4),B(3,2),C(3,1), D(3,1) and E (3,2) 
geometry
Find the area of a pentagon ABCDE with verticles A(0,4),B(3,2),C(3,1), D(3,1) and E (3,2) 
pentagon...GEOMETRY
ABCDE is a regular pentagon. FAD is an equilateral triangle, such that points F and E are on the same side of line AD. What is the measure (in degrees) of ∠FAB? 
maths
The convex pentagon ABCDE has a right angle at B,AB=BC andCD=DE=EA=1cm,AC=2cm.If AC and ED are parallel ,find the area of the pentagon. 
maths
ABCDE is a Pentagon with BE parallel to CD and BC parallel to DE. BC is perpendicular to CD. if the perimeter of ABCDE is 21cm. Find the value of x and y. 
Geometry
Regular pentagons A and B are similar. The apothem of Pentagon A equals the radius of Pentagon B. Compare the areas. The area of Pentagon A is equal to 1.49 times the area of Pentagon B. The area of Pentagon B is equal to 1.49 times … 
Geometry
Problem: ABCDE$\ is an equilateral pentagon with side length 2 in which angle B= angle E=120 degrees. The area of ABCDE can be expressed in the form square root of x + square root of y for some integers x and y. Find x+y. I don't understand. … 
Geometry
(SAT Prep) The perimeter of pentagon ABCDE is 30 in, AB = 7 in, BC = CD = 6 in, DE = 5 in. How many sides of the pentagon have equal length? 
Geo
(SAT Prep) The perimeter of pentagon ABCDE is 30 in, AB = 7 in, BC = CD = 6 in, DE = 5 in. How many sides of the pentagon have equal length?