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Syllabus

1) ABCD is a paralellogram. X and Y are mid points of BC and CD respectively.Prove that area (AXY) = 3/8 area(paralellogram ABCD)

2) In a triangle ABC P and Q are respectively the mid points of AB and BC and R is the mid point of AP. Prove that:

1) area(PRQ) =1/2 area(ARC)

2) area(RQC) = 3/8 area(ABC)

3) area(PBQ) = area(ARC)

(// means parallel)

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).

The line parallel to the parallel sides of a trapezium passing through the mid-points of the slant sides divide the trapezium into ratio 5:2. Then find the ratio of parallel sides

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

prove that median divides triangle into two equal parts

1-krishnasarp 2-parmanand 3-janmanth 4-bekhatke 5-bailghari

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

(i)ar(OMR)=1/2 ar(OQR)

(ii)ar(OMR)=1/4 ar(PQR)

(iii)ar(ONR)=ar(QMN)

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

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

ABCDis a quadrilateral.P and Q are the mid points of sides CD and AB respectivel. AP and DQ meet at X whereas Bp and CQ meet at Y. Prove that area of ADX+area of BCY=area of quadrilateral PXQY.

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

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

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.

3.A point E is taken on the side CD of a parallelogram. ABCD and CD is produced to F so that DF = CE. BE produced meets AD produced in G and the line through F parallel to AG is FH and H lies on produced part of BE. Prove that area of parallelogram AFHG = area of parallelogram ABCD.in a triangle ABC,E is the midpoint of median AD. Show that area of BED = 1/4 area of ABC

a farmer has a square plot of land where he wants to grow five different crops at a time . on half of the area in the middle he wants to grow wheat but in rest four equal triangular parts he wants to grow different crops.

a. explain by diagram how he can divide the area to fulfill his purpose .

b. by using this crop pattern which values are depicted by the farmer

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.

A triangle and rhombus are on the same base and between the same parallels then the ratio of the area of triangle to that of rhombus is

(A)1:1 (B) 1:2

(C) 1:3 (D) 1:4

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)

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).

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

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

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

ABCD is a rectangle and EFGH is a trapezium in the given figure. Prove that ar(ABCD) = ar(EFGH)

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)

Q24. In the given figure, ABCD is a parallelogram. AB is produced to a point P and DP intersects BC at Q. Prove that area ($\u2206$APD) = area (quad. BPCD)

[Hint : Diagonal divides a || gm into two triangles of equal area

$\therefore $ area $\u2206$ABD = area $\u2206$DBC

Again, area $\u2206$BPD = area $\u2206$BPC ($\because $ Triangles on the same base and between the same parallel are equal in area )

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.

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

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

Angle BOD = Angle AABCD 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

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 thatar ( AOD ) = ar ( BOC ). Prove that ABCD is a trapezium....!!I GuARAnTEeEE ThUMBS uP* FoR De CrrCt aNsaZz... ;)Q.E.Din R.D.Sharma(book)?He use it after proving every theorem.

(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.

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

abcdshow thatarea apb +area pcd = 1/2 area abcd

area apd +area pbc =area apb+area pcd

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.

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)

The semiperimeter of a triangle is 96 cm and its sides are in the ratio of 3:4:5. Find the area of the triangle.,

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)

Answer :the diagonals of a parallelogram ABCD intersects at O at a line through O intersect AB at X and DC at Y. prove that OX=OY

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

PQRS is a parallelogram. A, B, C and D are the mid points of sides PQ, QR, RS and PS respectively. If area of triangle DAC is equal to 10cm

^{2. }Find the area of triangle ABC.O is any point on the diagonal PR of a parallelogram PQRS . prove that ar(PSO) = ar(PQO) .

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 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 ABCis right angled at A. AL is drawn perpendicular to BC. Prove thatangle BAL =angle ACBArea of Triangle ABC is 800cm

^{2}. 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.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 the given figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If DBC55 and BAC45, find BCD.

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

Q.PQRS and PABC are two parallelograms of equal area. Prove that QC parallel to BR.

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

which PQ = PR = 20 cm and QR = 26 cm. If a

point O is marked on PS in such a way that

angle QOR = 90°, then the area of the quadrilateral

PQOR is approximately equal to

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)

Find the area of triangle ALM.

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.

if an angle of a parallelogram is three-fifth of its adjacent angle, find all the angles of a parallelogram.

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.

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

THE BASE BC OF TRIANGLE ABC IS DIVIDED AT D SO THAT BD=1/3 BC. PROVE THAT ar (triangleABD) =1/2 ar (triangle ADC).

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.

Diagonals of a parallelogram are 8m and 6m respectively. If one side is 5m, then the area of Parallelogram is

a)18m

^{2}b)30m^{2}c)24m^{2}d)48m^{2}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)

If ABCD is a parallelogram , then prove that : ar(ABD) = ar (BCD) = ar(ABC) = ar(ACD) = 1/2 ar(ABCD).