ABCD is a trapezium in which AB is parallel to DC. DC=30 cm. and AB=50cm. if  X  and Y   are respectively the mid points of AD and BC, prove that     (Nine times the area of DCYX= seven times the area of XYBA.)

 if the medians of a triangle ABC intersect at G show that ar ( AGB ) = ar(AGC)=ar(BGC)=1/3 ar(ABC).

prove that two triangles having the same base (or equal bases) and equal areas lie between the same parallels.

E is the midpoint of diagonal BD of Parallelogram ABCD.If the point E is joined to a point F on DA such that DF= 1/3 of DA ,then ratio of th area of triangle DFE to area of quadrilateral ABEF is

a) 1 : 3 b) 1 : 4 c) 1 : 5 d)2 : 5

prove that median divides triangle into two equal parts

ABCD is a trapezium with AB parallel to CD.LM is the line joining midpoints of AD and BC respectively.It is given that LM parallel to AB.Prove thatLM=1/2(AB+DC

The median BE and CF of a triangle ABC intersect at G. prove that area of triangle-GBC = area of quadrilateral AFGE.

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Diagonals AC and BD of trapezium ABCD with AB||DC intersect each other at O.

prove that ar(AOD) = ar (BOC)?

 prove that the diagonals of a parallelogram divides into four triangle of an equal area

ABCD is a parallelogram in which BC is produced to E such that CE = BC(Fig. 9.17). AE intersects CD at F.If ar (DFB) = 3 cm2, find the area of the parallelogram ABCD.

 How can we prove this as theorem:

Parallelogram with same base and having equal areas lie between the same parallel.

Please let me know the answer as fast as possible

in a triangle ABC,E is the midpoint of median AD. Show that area of BED = 1/4 area of ABC

The diagonals of a parallelogram ABCD intersect at point O. Through O, a line is drawn to intersect

AD at P and BC at Q. Show that PQ divides the parallelogram into two parts of equal areas.

Area of Triangle ABC is 800cm² . AD is a median, E is the mid point of AD. If F is the mid point of AB then find that area of Triangle AEF.

P and Q are respectively the mid points of side AB and BC of a triangle ABC and R is the mid point of AP show that,

{1} ar(PQR)= 1/2 ar(ARC)

{2} ar (RQC)=3/8 ar(ABC)

3) ar (pBQ) = ar(ARC)

Prove that area of a rhombus is half the product of its diagonals.

two consecutive angles of a parallelogram (x+60)degree ans(2x+30)degree. what special name can you give this parallelogram?

Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that

[Hint: From A and C, draw perpendiculars to BD]

Let ABC be an equilateral triangle in which coordinates of B and C are (5,0) and (-5,0) respectively . Find the coordinates of the oint A.

D is mid point of side BC of a triangle ABC and E is mid point of BD.If O is mid point of AE , then prove that ar(BOE)=1/8ar(ABC)

If E, F, G, H ar respectively the mid points of the sides of a parallelogram ABCD, show that ar(EFGH)= 1/2 ar(ABCD)

prove that a cyclic trapezium is always isosceles trapezium.

Prove that the line segment joining the mid-points of opposites sides of a quadrilateral bisect each other.

Please help me with these sums

In a parallelogram PQRS, L and M are the mid-points of QR and RS respectively. Prove that :

ar(ΔPLM) = 3/8 ar( IIgm PQRS).

Please help. :)

Parallelogram ABCD and rectangle ABEF are on the same base and have equal areas. Show the perimeter of parallelogram is greater than rectangle.

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ABC and BDE are two equilateral triangles such that D is the midpoint of BC .AE intersects BC in F.prove that::

1. ar(triangle BDE)=1/4 ar(triangle ABC)
2. ar (triangle BDE)=1/2 ar(triangle BAE)
3. ar (triangle BFE)= 2ar(triangle FED)
4. ar(triangle FED)=1/8 ar (triangle AFC)
5. ar(triangle ABC)=2ar(triangle BEC)
6. ar(triangle BFE)=ar (triangle AFD)
7. ar(triangle BFE)=2ar(triangle EFD)

A farmer has a plot of land in the shape of an eqilateral triangle of side 300m.He decides to give a part of his land which also is in the shape of an equilateral triangle of side 100m to his friend who is poor.But his friend refuses.So he takes a small amount as rent for his land but lets his friend take the produce.

Answers the following questions.

How could this be done? Explain with figure. Calculate tyhe area of equilateral field with side 300m

What part of the field has the farmer given to his friend in respect of area?

What value is depicted here?

Why did the friend refuse but agree afterwards?

If O is the circumcentre of Triangle ABC and OD prependicular to BC. Prove that

Angle BOD = Angle A

prove that in a triangle the line segment joining the mid points of any to sides is parallel to the third side.

Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that

ar ( AOD ) = ar ( BOC ). Prove that ABCD is a trapezium....!!

I GuARAnTEeEE ThUMBS uP* FoR De CrrCt aNsaZz... ;)

(1) D and E are points on sides AB and AC respectively of triangle ABC such that ar (DBC) = ar (EBC). Prove that DE//BC

(2) Diagnols AC and BD of a quadrilateral ABCD intersect at O in such a way that ar (AOD) = ar (BOC). Prove that ABCD is a trapezium

(3) Diagnols AC and BD of a quadrilateral ABCD intersect each other at P. Show that ar (APB) x ar (CPD) = ar (APD) x ar (BPC)

CAN SOMEONE PLZZZZ GIVE THE ANSWERS TO THESE QUESTIONS .vryy imp...

ABCD is a parallelogram.P and Q on BC trisects it.Prove that ar(APQ) =ar(DPQ)=1/6ar(ABCD)

 If each diagonal of a quadrilateral seperates it into two triangles of equal area, prove that the quadrilateral is a parallelogram.

if a square and a rhombus stand on same base , prove area of square has larger area

P and Q are any two points lying on the side DC and AD respectively of a parallelogram ABCD.Show that ar(APB)=ar(BQC).....

p is a point in the interior of a parallelogram abcd show that

area apb +area pcd = 1/2 area abcd

area apd +area pbc =area apb+area pcd

in a quadrilateral abcd , ad=9 cm, dc=17 cm, bc=8 cm find ab and the area of the quadrilateral?

If the mid points of the sides of a quadrilateral are joined in order, prove that the are of the parallelogram so formed will be half of the area of the given quadrilateral. Please experts answer it as quickly as possible.

WHAT IS AREA AXIOMS,CONGRUENT AREA AXIOMS,AREA MONOTONE AXIOM,AREA ADDITION AXIOM AND RECTANGLE AREA AXIOM

XY is a line parallel to side BC of a triangle ABC. If BEAC and CFAB meet at E and F repectively. Show that ar(ABE) = ar(ACF)

In figure, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, prove that ar(ABE)=1/2ar(ABC).

D, E and F are respectively the mid-points of the sides BC, CA and AB of a ΔABC. Show that

(i) BDEF is a parallelogram.

(ii) ar (DEF) = ar (ABC)

(iii) ar (BDEF) = ar (ABC)

Triangle ABC and DBC are on the same base BC with vertices A and D on opposite sides of BC such that area of triangle ABC = area of triangle DBC. Show that BC bisects AD

 O is any point on the diagonal PR of a parallelogram PQRS . prove that ar(PSO) = ar(PQO) .

I'm not able to solve this sum.... please can anyone help me?

Find the length of a chord which is at a disatnt of 8cm from the centre of a circle of radius 10 cm.

 ABCD is a quadrilateral. A line through D,parallel to AC meets BC produced in P. Prove that  area of triangle APD= area  of quadrilateral ABCD.

ABCD is a parellelogram AC is drawn parallel to ED . EC is joined

which of the folllowing is correct

(1)ar of triangle ADC= ar of triangle AED

(2)ar of triangle ADC= ar of triangle EDC

ABCD IS A PARALLELOGRAM, G IS THE POINT ON AB SUCH THAT AG = 2GB, E IS A POINT OF CD SUCH THAT CE = 2DE AND AND F IS A POINT OF BC SUCH THAT BF = 2FC. PROVE THAT

1) ar(ADEG) = ar(GBCE), 2) ar(EGB) = 1/6 ar(ABCD) , 3) ar(EFC) = 1/2 ar(EBF) , 4) ar(EBG) = ar(EFC) , 5) FIND WHAT PORTION OF THE ARE OF PARALLELOGRAM IS THE AREA OF EFG.

A triangle ABC is right angled at A. AL is drawn perpendicular to BC. Prove that angle BAL = angle ACB

ABCDE is a pentagon.A line passing through B parallel to AC meets DC produced at F.Show that

ar(ACB)=ar(ACF)

ar(AEDF)=ar(ABCDE)

explain with figure

 prove that parallelogram on the same base and between the same parallel are equal in area

In triangle PQR, PS and RT are medians and SM is parallel to RT. Prove that QM= 1/4 PQ.

The circumcentre of the triangle ABC is O. Prove that angle OBC+angle BAC=90 degree. Please answer fast!!!!!!

ABC and ABD are two Triangles on lthe same base AB. If line segment CD is bisected by AB at O, Show that ar(ABC) = ( ABD)

 experts plshh give me the proof of all three theorems ,,, ??? faster i need it !!!

i mean theorem 9.1 , 9.2 and 9.3 ??? 

A point E is taken on the side BC of a parallelogram ABCD. AE and DC are produced to meet at F.

Prove that ar( ADF ) = ar (ABFC ).

In triangle ABC, AD is the median and DE || AB. Prove that BE is another median.

Please help! :O

Sorry, i couldn't post the figure.

 ABCD is a trapezium with AB parallel to DC. a line parallel to AC intersects AB to X and BC to Y. prove that ar(ADX)=ar(ACY).

The diagonals of quad. ABCD intersect at O .Prove that if BO = OD, then ar (triangle ABC) = ar (triangle ADC).

If a triangle and a parallelogram are on the same base and between the same parallels, then prove that area of the triangle is equal to half the area of the parallelogram.

My teacher is saying that it is a theoram plz tell me by proving it...

If a triangle is divided into four pieces with areas 8 , 5 , 10 and x then find x.

1. in triangle ABC.D id the mid-point of AB &P is any point on BC.if CQ is parallel to PD meets AB in Q,then prove that :-

ar(BPQ)=1/2ar(ABC

 the base of a triangular field is three times its altitude.if the cost of sowing the field at rs 58 per hectare is rs 783,find its base and height.

ABCD is a parallelogram and BC is produced to point Q such that AD=CQ. If AQ intersects DC at P, show that ar(triangle BPC)=ar(triangle DPQ)