# geometry

posted by .

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.

• geometry -

let the intersection of AE and DB be K
So triangles ADE and ADG have the same base AD and the same height , since parallel lines are equal distances apart.
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

• geometry -

tri FDG

• geometry -

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

• geometry -

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
Therefore AR (ABP) =AR(ACQ)

• geometry -

Jabbba jabba kappale mayathu

• geometry -

This question is wrong

## Similar Questions

1. ### 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.
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)
3. ### 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)
4. ### 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?
5. ### 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.
6. ### 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.
7. ### 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 …
8. ### 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. …
9. ### 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?
10. ### 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?

More Similar Questions

Post a New Question