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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).

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}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

6. Find the surface area of a sphere having diameter 30 cm.

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

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

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

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

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.

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

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 parralelogram, in which angle DAB= 30, AB=20cm and BC=20cm. Find the area of the parallelogram.

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

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

(// means parallel)

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.

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

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.

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 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 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

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)

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 )

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)

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

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

Parallelogram ABCD and rectangle ABEF are on the same base and have equal areas. Show the perimeter of parallelogram is greater than rectangle.

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

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

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

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

Angle BOD = Angle A^{2}. If its base is twice the corresponding altitude, determine the base and altitude.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... ;)If a planar region formed by a figure T is made up of two non overlapping planar regions formed by figures P and Q ,then ar(P)+ar(Q),where ar(X) denotes the area of figure X

Thank you

(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

ABCD is a parallelogram, AB = 14cm, BC = 18cm, and AC = 16cm. Find the length of the other diagonal.

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)

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

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

A right triangle PQR with sides 3cm, 4cm, and 5cm is revolved about the side length 4cm. Find the volume of the shape so generated.

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.

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.

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

what is the answer of the following question:-

in a parallelogram ABCD, P,Q,R,S are mid- points of the sides AB, CD, DA, and BC respectively. AS, BQ, CR, and DP are joined.Find the ratio of the area of the shaded region to the area of parellogram ABCD.

figure is given Below in picture

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.

a) Circumcentre b) midpoint of the hypotenuse c) internal point of the triangle

Please! Expiain me clearly with diagram.

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)

In a cyclic quadrilateral PQRS if angle P-angleR =50degree then find the measure of angle p and angle r.

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 ).

AB and CD are two parallel chords of a circle whose diameter is AC. Prove that AB=CD. Please reply ASAP. I have an exam.

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).

[Hint: Join BG]

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...

ar(BPQ)=1/2ar(ABC

Prove that the area of parellelograms is the product of any its sides and the corresponding altitudes .

please provide the whole proof !!!!!!

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)

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