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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.)

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.

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

prove that median divides triangle into two equal parts

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

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

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

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

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

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

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

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

Draw the frequency polygon representing the following frequency distribution: -

Diff. b/w the outer lateral surface area and inner lateral sur. area of cylindrical metallic pipe 28 cm long is 176 sq. cm.Find the outer and inner radii of the pipe, if the pipe is made 352 cubic cm of metal.

Construct an isosceles triangle whose perimeter is 12 cm and altitude is 4 cm.

If the non parallel sides of trapezium are equal prove that it is cyclic.

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.

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

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

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.

IN triangle ABC points M and N on side AB and AC respectively are taken, so that AM=1/4 AB and AN=1/4AC.Prove that MN =1/4BC.

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.

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.

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)

What does ar(....) mean?

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)

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 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

THESEMI PERIMETER OF A TRIANGLE IS 96cm. ITS SIDES ARE IN THE RATIO OF3:4:5.FIND AREA OF THE TRIANGLE.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.

Find the area of triangle ALM.

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

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

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

Angle BOD = Angle A(// means parallel)

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

In the fig. triangle ABC is right angled triangle right triangle at A. BCED, ACFG and ABMN are squares on the line BC, CA and AB resp. line segment AX peprendicular DE meets BC at Y. Show that

i. Ar(BYXD) = 2ar(triangle MGA)

ii. ar (CYXE) = ar(ACFG)

iii. ar(BCED) = ar(ABMN) + ar(ACFG)

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... ;)(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.(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...

[Hint: Join BG]

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

the diagonals AC and BD of a ||gm ABCD meet at O. from mid-point of AD, a line MH is drawn || to DB meetiong AO at H and a line MK||AO meeting DO at K. prove that ar(||gm MHOK) = 1/16 ar(||gm 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).....

ar(ABCD)+ar(AEFB)=ar(EFCD)

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.

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}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)

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 :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.

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

ABCD is a quadrilateral in which the bisectors of angleA angleC meet DC produced at Y and BA produced at Y respectively. Prove that AngleX + AngleY = 1/2 (angleA+AngleC)

Please answer this question urgently. My exam is on 20

^{th}Thursday.Thanks

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

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=

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.

^{2}, find ar( triangle ZYR)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 ACBar(BPQ)=1/2ar(ABC

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

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.

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

ABCD is a parallelogram, G is the point on AB such that AG = 2GB, E is a point of DC , such that CE = 2DE and F is the point of BC such that BF = 2FC. prove that :

1) ar (quad ADEG) = ar(quad GBCE)

2.) ar( triangle EBG) = 1/6 ar( quad ABCD)

3) ar( triangle EFC) = 1/2 AR(triangle EBF)

4 ) ar( triangle EBG )= ar( triangle EFC)

5 ) find what portion of the area of parallelogram is the area of triangle EFG.

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

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

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 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).

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).

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 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...

Q. In the given figure, ABCD is a parallelogram and E and F are the sides DC and AB respectively. show that $\text{ar}\left(\u25b3AEF\right)=ar\left(\u25b3CFE\right)$.

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)

prove that 'median divides a triangle into two triangles of equal area.' Plzzzzzzz hurry up frdz, tomorrow is my test!!!!!!!!!!!!