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Syllabus

Explain the converse of midpoint theorem.

How to prove all the theorems of chp 8 Quadrilaterals

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}?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.]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 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.

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

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)_{}angle COD =78 then find the value of angle OABshow that the quadrilateral formed by joining the midpoints of the consecutive side of a square is also a square

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 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

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

No links plz.

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

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

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

urgent

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

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 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 a quadrilateral ABCD, angle A +angle C is 2 times angle B + angle D. if angle A = 40 degree,then angle B =

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.

STATE AND PROVE MIDPOINT THEOREM

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

90, 20, 40 or 70.

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

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.

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

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 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?

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 ?

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

In a quadrilateral ABCD, AB=CD and angle B=angle C. Prove that AD parallel to BC.

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?

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

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.

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?

Q. In the figure, ABCD is a parallelogram. Points A, B, E and F are collinear and AB = EF. Prove that DEFC is a parallelogram.

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

(i) AB = 2AP

(ii) AM = 2AR

(iii) BM = 2PR

(iv) BC = 4PR.

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.

In a trapezium PQRS, PQ || SR, PQSR. X and Y are the midpoints of SP and QR respectively. If XY = 7.5 and PQ = 12, then find RS.

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)

pls explain mid point theorem used in the video above

ABCD is a parallelogram and X is the midpoint of D and Y is the midpoint of BC. Prove that XY and BD bisect each other..

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 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.

PQRS is a rhombus with angle PQR = 58.Determine angle PRS

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.

Please answer fast.

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

Given A rectangle WXYZ in which M is the mid point of WX

Prove that ZMY is isosceles

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.

The angle between the two altitudes of parallelogram through the vertex of an obtuse angle is 50 degree. Find the angles of parallelogram.

Reply fastttttttt

Points

andAare in the same side of a lineB.landADare perpendiculars toBE, meetinglatlandDrespectively.Eis theCmid pointof line segment.AB.Proove that CD = CEwhat 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.

Prove that quadrilateral formed by bisectors of the angles of a parallelogram is a rectangle.