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Syllabus

Explain the converse of midpoint theorem.

How to prove all the theorems of chp 8 Quadrilaterals

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.

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)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.

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

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

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 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 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

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?

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.

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?

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)

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 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.

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 = 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.