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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)

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

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

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

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

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

Q9)Use the following information to answer the next question.

The given figure shows a quadrilateral ABCD. A line drawn from A parallel to BD intersects CD produced at Q. BP is a line parallel to CQ such that QP⊥BP.

If CQ = 22 cm and PQ = 5 cm, then what is the area of quadrilateral ABCD?

OptionsMark for review55 cm

^{2}65 cm

^{2}165cm

^{2}220 cm

^{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.

Find the area of a parallelogram whose adjacent sides are 50cm and 60cm and one of its diagonals is 70cm.

1. EXISTENCE POSTULATE

Corresponding to each polygon P lying in a plane, there exists a real number ar(P) $\ge $ 0, called its area.

2. DOMINANCE POSTULATE

For regions ${R}_{1}and{R}_{2}$ in a plane, if ${R}_{1}\subseteq {R}_{2}$, i.e., if ${R}_{1}$ is a part of ${R}_{2}$ then ar(${R}_{1}$) $\le $ ar(${R}_{2}$).

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

please answer it please tommorow is my sa 2 triangle ABC and ABD are two triangles on the same base AB. if line segment CDis bisected by AB at O. show that ar(ABC)=ar(ABD).

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.

prove that of all parallelograms of which the sides are given,the parallelogram which is rectangle has the greatest area.

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.

(a) area of triangle EDC = 2/9 area of triangle ABC

(b) area of triangle FBD = 2/7 area of AFDC

(c) area of triangle DEF = 2/9 area of triangle ABC

(d) area of triangle(EDC + DBF + AFE) = 2 area of triangle DEF

EXPERTS PLS ANSWER AS QUICK AS POSSIBLE WITH THE REASON ALSO.

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

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

i) ar (ABEF)

ii) ar (ABD)

iii) ar (BEF)

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)

(b) ABCD is a parallelogram. BP and DQ are the perpendiculars from B and D on the diagonal AC.

(i) Show that BP = DQ.

(ii) Show that

ar ($\u25b3$ADX) = ar ($\u25b3$ABX), where X is any point in AC.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)

Traingles ABC & DBC are on the same base BC with vertices A & D on opposite sides of BC such that ar ABC = ar DBC. Show that BC bisects AD.

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

ABCD is a parallelogram and line through A cuts DC at P and BC produced at Q . Prove that area of triangle QPC=area of triangle DPQ.

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::

Manisha has a garden in the shape of a rhombus. The perimeter of the garden is 40m and one of its diagonal is 16m. She wants to divide it into two equal parts and use these equal parts for growing vegetables and wheat separately. Find the area of each part of the garden.

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

Angle BOD = Angle AABCD is a parallelogram whose diagonals intersect each other at right angles.If the length of diagonals is 6cm and 8cm.find lengths of all the sides of parallelogram.

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

THE AREA OF FIGURE FORMED BY JOINING MIDPTS OF ADJACENT SIDES OF A RHOMBUS WITH DIAGONALS 12CM AND 16 CM

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... ;)din't got the meaning of this ques..

XY is a line parallel to side BC of a triangle ABC. If BE || AC and CF || AB meet XY at E and E respectively, show that

ar (ABE) = ar (ACF)

(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 having area of 450cm square.If ABllCD,P and Q divide AB and CD in the ratio 1:2, find the area of the parallelogram APQD and parallelogram PBCQ.

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 the sides of a parallelogram are b1 and b2 and distance between two sides is h, then show that area is =1/2*h(b1+b2)

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

Ajit don't try to contact with me plz

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.

Show that a median of a triangle divides it into two triangle of equal area.

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)

What does ar(....) mean?

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 :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

Given two points Aand B and a positive real no. x. Find the locus of point P such that area(tri. PAB)=x

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

5. a craft mela is organised by welfare association to promote the art and culture of tribal people. the pandal is todecorated by using string of bulbs all aroung the field . there are two options either to arrange it in a rectangular field . there are two options either to arrange it in rectangular field ABEF or parallelogrm ABCD with equal area

a. what shape of the field should be chosen to minimise the expense of bulb and why?

b. which values are depicted here ?

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.

Q1. PQRS IS A PARALLELOGRAM. POINTS A AND B ARE TAKEN ON PQ SUCH THAT PA=AB=BQ AND PS//AD//BC. PR IS JOINED. PROVE THAT AR(PAE)=AR(CFR)

A triangle ABCis right angled at A. AL is drawn perpendicular to BC. Prove thatangle BAL =angle ACBPSQR is a parallelogram in which angle PSR=125

^{0},angle RQT=????????? angle RQT is exterior angle>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 of all parallelograms of which the sides are given, the parallelogram which is rectangle has the greatest area

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

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...

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

Draw a line segment AB =5cm. from the point A draw a line segment AD = 6cm making an angle of 60 degree.draw perpendicular bisector of AD.

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

show that diagonal of a parallelograms divide it into two congruent triangles

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)

Parallelogrom ABCD and rectangle ABEF have the same base AB and also have equal areas.Show that the perimeter of the parallelogram is greater than that of the rectangle.

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 ).

a quadrilateral ABCD is such that diagonal BD divides it areas in two equal parts prove that BD bisects AC

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.

ABCis a trangle, D is midpoint of AB, p is any point on BC. Line CQ is parallel toPD to intersect AB at Q. PQ is joined.

pt ar(bpq) = 1/2 ar(abc)

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).

ABCD is a trapezium in which AB is parallel to DC such that AB = a cm and DC = b cm. If E and F are mid point of AD and BC respectively.Then, ar (ABFE):ar (EFCD) = ?

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

in a given fig PQRS is a parallelogram and the line segment PA and RB bisect the angles P and R respectively show that PA parallel RB

short method of Q5 of exercise 9.4

ar(BPQ)=1/2ar(ABC

ABCD is a parallelogram X and Y are the mid points of Bc and CD respectively. Prove ar(AXY)=3/8ar(ABCD)

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)