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Syllabus

Explain the converse of midpoint theorem.

How to prove all the theorems of chp 8 Quadrilaterals

ABCD is a square. Determine Angle DCA.

ABCD is a trapezium in which AB || CD and AD = BC (see the given figure). Show that

(i) ∠A = ∠B

(ii) ∠C = ∠D

(iii) ΔABC ≅ ΔBAD

(iv) diagonal AC = diagonal BD

[

Hint: Extend AB and draw a line through C parallel to DA intersecting AB produced at E.]4.during maths lab activity each student was given four broom sticks of lenths 8 cm , 8cm, 5cm ,5cm to make different types of quadrilaterals .

a. how many quadrilaterals can be formed using these sticks

b. name the types of quadrilaterals formed

c. while doing this activity which value is depicted

Prove that the quadrilateral formed by joining the midpoints of consecutive sides of rectangle is a rhombus and PLEASE PROVE THE VICE-VERSA ALSO.

Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

pls explain.

show that the diagonal of a square are equal and bisect each other prependicularly

In ABC, D is the mid-point of

AB and P is any point on BC. If CQ || PD meets AB inthen prove that ar (BPQ) =1/2ar (ABC)3. a class teacher gave students coloured papers in the shape of quadrilateral . she asked them to make parallelogram from it usingpaper folding .

a. how can a parallelogram be formed by using paper folding ?

b. prove that it is a parllelegram ?

c. what values are depicted here ?

show that the quadrilateral formed by joining the midpoints of the consecutive side of a square is also a square

explain midpoint theorem with te solving of example

Prove that the line segment joining the mid-points of the diagonals of a trapezium is parallel to each of the parallel sides and is equal to half the difference of these sides.

Diagonals AC and BD of a quadrilateral ABCD intersect each other at P.Show that ar (APB) x ar (CPD) = ar (APD) x ar (BPC

In a parallelogram show that the angle bisectors of two adjacent angles intersect at right angles

ABCD is a rhombus with angle ABC =40. The measure of angle ACD is what?

90, 20, 40 or 70.

show that the line segment joining the mid point of the opposite sides of a quadrilateral bisect each other

please prove the mid point theorem

In the figure, ABCD is a rhombus whose diagonals meet at O. Find values of x and y.

in a quadrilateral pqrs ,the bisectors of angle R and angle S meet at point T.

Prove that angle P+ angle Q= 2angle RTS

in a quadrilateral ABCD , AO and BO are the bisectors of angle A and angle B respectively. Prove that angle AOB = 1/2 (angle C+ angle D)

ABCD is a parallelogram,P and Q are points on DC and AB respectively,such that angle DAP=angleBCQ.Show that Acqp is a parallelogram.

prove that if the diagonals of a parallelogram are equal,then its a rectangle

prove that diagnals of a rectangle are of equal length

AD and BE are medians of triangle ABC and DF parallel BE.Prove that CF =1fourth AC?

in a cyclic quadrilateral PQRS if angle p = 80 degree then angle r = ? pls give the steps for the problem

in the given figure, ABCD is a square. if angle PQR=90 and PB=QC=DR, prove that QB=RC, PQ=QR and angle QPR=45

In triangle ABC, D, E and F are respectively the mid-points of sides AB, BC, CA. show that triangle ABC is divided into four congruent triangles by joining D, E, and F.

3. in a square ABCD, the diagonals AC and BD bisect at O. then triangleAOB is

a)acute angled

b)right angled

c)obtuse angled

d)equilateral

STATE AND PROVE MIDPOINT THEOREM

Given 4 points A, B, C, D such that 3 Points A, B, C are collinear. By joining these points in order we get

a) a rhombus b) a rectangle c) a square d) a straight line

pls give an explanation along with the ans.

ABCD is a rectangle in which diagonal AC bisects angle A as well as angle C.show that

i) ABCD is a square

i) Diagonal BD bisects angle B as well as angle D

1. How the angle bisector of a parallelogram form a rectangle?

2. If an angle of parallelogram is two-third of its adjacent angle. find the angles of the parallelogram?

3. Find the measures of all the angles of a parallelogram is one angle is 24 degree less than twice the smallest angle?

4. AB and CD are two parallel lines and a perpendicular angle intersect AB at X and CD at Y. Prove that the bisector of the interior angle form a rectangle?

5. ABCD is a parallelogram and line segment AX bisects the angle A and C respectively, show that AX II CY.

6. Given ABC, lines are drawn through A, B, and C respectively parallel to the side BC, CA and AB forming triangle PQR. Show that BC = 1/2 QR.

7. BM and CN are perpendicular to a line passing through the vertex A of a triangle ABC, if the angle is the midpoint of BC. Prove that angle M = angle N.

M and N are the mid-points of non parallel sides of a trapezium PQRS. prove that (i) MN is parralel to PQ, (ii)MN= 1/2 (PQ+RS).

Prove that the opposite angles of an isosceles trapezium are supplementary?

Please help me with this question! :O

BC = 10 cm. Find the length of the diagonal BD

ABCD is a parallelogram in which P is the midpoint of DC and Q is a point on AC such that CQ=

^{1}/_{4}AC. If PQ produced meet BC att R, prove that R is the midpoint of BC.PQRS is a rhombus with angle PQR = 58.Determine angle PRS

ABCD is a rhombus and AB is produced to E and F such that AE=Ab=BF.Prove that ED and FC are perpendicular to each other.

What is the difference between Rhombus and Kite?

In a square ABCD, F and E are any points on CD and CB respectively such that, AF = DE. Prove that angle EPF = 90 degrees.

Please please help me in this sum. My head is breaking.

ABCD is a //gm and line segment AX and CY bisects angles A and C respectively where X is a point on AB. To prove AX // CY

AD is the median of the triangle ABC and E is the midpoint AD, BE produced meets AC in F. Prove that AF=1/3 AC?

Q. In the given figure, $\text{AB}\parallel \text{CD\u2225EF\u2225GHandHF=FD=DB}$. If AC = 1.5 cm, find AG.

Please, prove that an isosceles trapezium is a cyclic quadrilateral.

let ABC be an isosceles triangle in which AB = AC. if D, E, F be the mid-points of the sides BC, CA and AB respectively, show that the segment AD and EF bisect each other at right angles.

the diagnol of a rectangle PQRS meet at point O.if anglePOQ=124.find angleOSR

Each side of a rhombus is 10 cm long and one of its diagonals measures 16 cm. Find the length of the other diagonal and hence find the area of the rhombus

ABCD is a trapezium in which AB || CD & AD=BC. Show that

(i) ∠A = ∠B

(ii) ∠C = ∠D

(iii) ΔABC ≅ ΔBAD

(iv) AC = BD

Please check my solution thoroughly and do any rectifications if needed.

No links plz.

ABCD is a rhombus.show that diagonal AC bisects angle A as well as angle C and diagonal BD bisects angle B as well as angle D?

sir/maam kindly tell me how to solve this question with proper steps?

if the diagonals of a quadrilateral bisect each other then it is a parallelogram

in triangle ABC in which ab=2ac . ba isproduced to d and exterior angle cad is bisected by ae cutting bc produced in e. Prove that c is the mid point of be

Points A and B are in the same side of a line l. AD and BD are perpendiculars to l, meeting at D and E. C is the midpoint of AB. Prove that CD = CE.

In ABCD Parallelogram, CD=(2x+1)cm and AB=(3x-2)cm, angle DAC = 60 degree, angle ABC = 105 degree. So angle CAB =?and Find the value of x

diagonals ACand BD of quadrilateral ABCD intersect at O such that OB = OD. if AB = CD , then show that :

1.ar(DOC) = ar(AOB).

2.ar(DCB) = ar(ACB)

3.DA ll CB or ABCD is a parallelogram.

^{2}-4=0E and F are respectively the mid-points of the non-parallel sides AD and BC of a trapezium ABCD.Prove that EF is parallel to AB and EF=1/2(AB+CD)

pls explain mid point theorem used in the video above

abc is an isosceles triangle in which ab=ac.ad bisects exterior angle pac and cd is parallel to ab.show that angle dac=angle bca and show that abcd is a parallelogram

ABCD is a paralleogram.AM and BN are respectively,the perpendiculars from A and B to DC and CD produced.Prove that AM =BN.

ABCD is a parallelogram in which angle A = 60 degree, if the bisectors of angle A and angle B meet DC at P, prove that (i) angle APB = 90 degree (ii) AD = DP and PB = PC=BC (iii) DC = 2AD

P,Q,R are respectively the mid points of sides BC,CA and AB of atriangle ABC.PR and BQ meet at X..CR and PQ meet at Y.Prove that XY=1/4 BC.

a. is this distribution fair? justify?

b. what value is depicted her?

In triangle ABC ,BM and CN are perpendiculars from B and C respectively on any line passing through A. If L is the mid point of BC , prove that ML = NL.

prove that the straight line joining the midpoints of the diagonals of a trapezium is parallel to the parallel sides of the trapezium and is equal to half their difference

the diagonals of a rectangle ABCD meet at O. IF angle BOC = 44, find angle OAD.

show that if the diagonals of quadrilateral bisect each other at right angles, then it is a rhombus.

Points

andAare in the same side of a lineB.landADare perpendiculars toBE, meetinglatlandDrespectively.Eis theCmid pointof line segment.AB.Proove that CD = CEIf two non parallel sides of a trapezium are equal then prove that it is cyclic quadrilateral.

what is the difference between

rhombus and a square

In any triangle ABC, BP and CQ are perpendiculars on any line through A and M is the mid-point of the side BC. Show that MP=MQ

ABCD us a rectangle. Find the values of x and y in each case.

figure is like this

AB is base and angle A is 35 degree

DC is opposite site

AC and BD is diagonal and intersent on O in mid pint and DOC is formed Y degree and BOC is formed X degree

In a figure, PQRS is a parallelogram and angle SPQ=60 degreee. If the bisectors of angle P and angle Q meet at A on RS, prove that A is the midpoint of RS...

Prove cyclic trapezium is isosceles and its diagonals are equal to each other.