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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)

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 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).

if ABCD is a rectangle inscribed in a quadrant of a circle of radius 10cm. if AD=2√5,find the area of the retangle.

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

An artist is designing a pattern of triangular tiles to cover a wall. Each section of the pattern is identical to the section shown here. If the wall is 576 cm long and 384 cm high, how many black tiles will the artist need to use on the wall ?

prove that median divides triangle into two equal parts

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

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

If X is the midpoint of the side BC of a parallelogram ABCD ,DX meets AC in Y.Prove that ar(triangle ADY) = AR(triangle DYC)

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

(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.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.

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

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

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

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.

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.

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.

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)

if perimeter of a right angled triangle is six times its smallest side,then the three sides of this triangle are in the ratio of

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

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

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

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

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)

There is a triangle ABC. A line is joining the virtice A to the triangles base BC at point D and is forming a media. E is any point on the median of triangle.Show that the area of ABE=area of ACE

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)

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.

in parallelogram ABCD,angle D =135,determine the measure of other angles.

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

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 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.

Two sides AB,BC & median AL of triangle are respectively equal to PQ,QR &PM of PQR. Show that (i)triangle congruent to triangle PQM (ii)triangle ABCcongruent triangle PQR.

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... ;)In triangle ABC, if L and M are the points on AB & AC respectively, such that LM is parallel to BC. If BM & CL intersect at O, prove that area of traingle LOB = area of triangle MOC.

(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...

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

ABCD is a parallelogram in which BC is produced to E such that CE =BC. AE intersects CD at F . Show that area OF TRIANGLE BDF = 1/3 of area(ABCD).

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

The second teachers video was very helpfull

i understood everything and hat too in easier method than my teacher

thanx meritnation for this awesome video!!!11

:D

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

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

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.

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

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 video of the lesson areas of parallegramam andtriangles are not clear sir. please see to this problem sir.

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 :abcd is a parallelogram and o is any point in it1s interior.prove that 1)ar(dob)=ar(cod) and 2)ar(boc) =ar(aod)

ABCD is a trapezium with parallel sides AB=a cm,CD=bcm.E and F are the mid points of non-parallel sides.The ratio of ar(ABFE) and ar(EFCD) is:

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

PQRS is a parallelogram, AB || PS and meets PQ at A and SR at B. o is any point on AB. Prove that ar(triangle SOR)+ar(triangle POQ)=ar (triangle SAR).

please answer ASAP

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 resident welfare society has developed a land having quadrilateral shape of sides 12 cm, 5 cm, 11 cm, 5 cm and diagonal 13 cm divide the land into two parts along diagonal, in one part they developed gardening and in another they developed classical musical institute.

(a) Find the areas of both parts of a land.

(b) What conclusion you will draw through this activity?

A triangle ABCis right angled at A. AL is drawn perpendicular to BC. Prove thatangle BAL =angle ACBABCDE 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)

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).

Prove that:A Diagonal of a parallelogram divides it into two congruent triangles.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...

find the area of the triangle whose sides are 42 cm, 34 cm, and 20 cm in length. hence, find the height corresponding to the longest side??

ar(BPQ)=1/2ar(ABC

plz explain the 1 st sum in the lets review which is :

in IIplz answer^{gm}PQRS , RN is perpendicular to PS and PM is perpendicular to SR .if PQ = 120 cm , PM =30root5 cm and RN = 180root5 cm , thn what is the measure of the side PS ?...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)

q-3] The surface area of a sphere & a cube are equal. Prove that their volumes are in the ratio 1:v22/7/6.[paye=22/7].

q-4] The area of 3 adjacent faces of a cuboid are x,y,z.. if the volume is v , prove that [v]2=xyz.

q-5] Wall paper ,312cm long and 25cm wide is required to cover the wall of a room . length of the room is 7m and its breadth is twice its height. Determine the height of the room .