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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)

In the given figure, D, E, F and G are the midpoints of AE, AB, AG and AC respectively. Then the Ar( triangle ADF): Ar( DEGF): Ar( EBCG) is equal to?

OPTIONS:

(1) 1:2:3

(2) 1:3:4

(3) 1:3:12

(4) 1:4:8

FIGURE TO THIS QUESTION IS ATTACHED BELOW.

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.

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 median divides triangle into two equal parts

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

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

Area 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.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

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 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.

abcd is a parallelogram, the angle bisectors of angle A and angle B intersect at O.Find the measures of angle AOD.

(// means parallel)

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

line segment joining the vertices of 2 tri is bisected by their common base , on opp. sides of which these vertices lie. prove that these triangles are equal in area

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.

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.

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

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

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)

In the given figure, D, E, F, G, are the midpoints of AE, AB, AG, AC respectively, then the Ar( triangle ADF) : Ar( DEGF) : Ar( EBCG) is equal to

OPTIONS:

(1) 1:2:3

(2) 1:3:4

(3) 1:3:12

(4) 1:4:8

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)

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

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. :)

in the given figure abcd is a parallelogram, ap is perpendicular to dc and cq is perpendicular to ad. if ab=10cm, ad=8cmand ap=8cm then cq=

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::

[Hint: Join BG]

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

Angle BOD = Angle Aprove that in a triangle the line segment joining the mid points of any to sides is parallel to the third side.

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

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... ;)(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)

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.

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

Q.E.Din R.D.Sharma(book)?He use it after proving every theorem.

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).....

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.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.

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.

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)

Find the area of triangle ALM.

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

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

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

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

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.

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.,

THESEMI PERIMETER OF A TRIANGLE IS 96cm. ITS SIDES ARE IN THE RATIO OF3:4:5.FIND AREA OF THE TRIANGLE.A triangle ABCis right angled at A. AL is drawn perpendicular to BC. Prove thatangle BAL =angle ACBIn triangle PQR, PS and RT are medians and SM is parallel to RT. Prove that QM= 1/4 PQ.

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

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

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

^{2}, find ar( triangle ZYR)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)

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

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.

P

C __________________________B

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Q /____________/R

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A

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).

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

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...

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

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

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

ar(BPQ)=1/2ar(ABC

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 that

LM=1/2(AB+DCthe 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.

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 )

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)