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Syllabus

Explain the converse of midpoint theorem.

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

How to prove all the theorems of chp 8 Quadrilaterals

a. is this distribution fair? justify?

b. what value is depicted her?

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.]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.

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 ?

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)Q. ABCD is a square of side 2 cm and E,F,G and H are the midpoints of the sides. What is the area of square PQRS in cm

^{2}?show that the quadrilateral formed by joining the midpoints of the consecutive side of a square is also a square

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.

_{}angle COD =78 then find the value of angle OABDiagonals 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

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

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

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

No links plz.

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

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)

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

ABCD is a rhombus AC=16cm ; BC=10cm. Find the length of the diagonal BD.

prove that diagnals of a rectangle are of equal length

ABCD is a parallelogram in whcih angle BAO = 35 degree, angle DAO = 40 degree and angle COD = 105 degree ,

calculate (i) angle ABO =

(ii) angle ODC

(iii) angle ACB

(iv) angle CBD

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

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.

in a quadrilateral ABCD, AB=BC & CD=DA then the quadrilateral is a

STATE AND PROVE MIDPOINT THEOREM

explain midpoint theorem with te solving of example

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.

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

Please help me with this question! :O

Each interior angle of a regular polygon is 144 degrees. Find the interior angle of a regular polygon which has double the number of sides as the first polygon.

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.ABCD is a trapezium. Angle D =(2x+10)degree, Angle A=(x+20)degree, angle C=92 degree, find the values of x and angle B

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?

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?

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

answer the following:-

1)in a parallogram ABCD, AB=10 cm and AD=6 cm. the bisectors of angle A meets DC in E. AE and BC produced meet at F. find the length of CF.

2)P,Q,R and S are respectively the mid-points of the sides AB,BC,CD and DA of a quadrilateral ABCD such that AC is perpendicular to BD and AC=BD. prove that PQRS is a square

3)ABCD is a quadrilateral in which AB||DC and AD=BC. prove that angle A =angle B angle C= angle D.

This is the question which was half answered . please help....

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.

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

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?

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

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

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.

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.

E 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)

prove that the diagonals of a rhombus are perpendicular to each other

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

Prove that -

By joining the mid-points of adjacent sides of a trapezium, four similar triangles are obtained.Thank youABCD 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

O is the point inside a rhombus ABCD such that BO = OC . prove that AO and OC are in same straight line

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.

LMNO is a trapzium with LM II NO If P and Q are the mid point of LO andf MN respectively. and LM=5 cm and ON=10 cm, calculate PQ.

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

(i) AB = 2AP

(ii) AM = 2AR

(iii) BM = 2PR

(iv) BC = 4PR.

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

Please check my solution and do any rectifications if needed.

No links plz.

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 = CEO is the point inside the rhombus ABCD such that BO=DO.Prove that AO and CO are in the same straight line.

what is the difference between

rhombus and a square

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

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