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Syllabus

Explain the converse of midpoint theorem.

_{}angle COD =78 then find the value of angle OABHow 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.]In a parallelogram LEFT,the bisector of angle L also bisects EF in P. Prove that LT =2LE. please answer it

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

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

pls explain.

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.

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)the diagonals AC and BD of a rectangle ABCD intersect each other at P. if angle ABD = 50 degree, then angle DPC =

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

the diagonal PR of a parallelogram PQRS bisect the angle R . prove thatPQRS is a rhombus.

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.

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

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

(i) ∠DAG (ii) ∠FEG (iii) ∠GAC (iv) ∠AGC

[Hint. (i) ∠EDA = 90° + 56° = 146°, ED = AD.]

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

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

No links plz.

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)

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

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

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

prove that diagnals of a rectangle are of equal length

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

90, 20, 40 or 70.

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

three angles of a quadrilateral measure 56

^{0 },115^{0}and 84^{0}.find the measure of the fourth angle.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.

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

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

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

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.

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.

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

Please help me with this question! :O

pqrs is a parallelogram px and qy are respectively the perpendiculars from p and q to sr and rs produced.prove that px =py

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

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

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?

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

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

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

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.

and angle A : angle C = 5:6. Find all the angles of the quadrilateral

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

Prove that :

(i) AECF is a parallelogram

(ii) BEDF is a parallelogram

(iii) PEQF is a parallelogram

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?

Q99. If A : B = $\frac{1}{2}:\frac{3}{8},\mathrm{B}:\mathrm{C}=\frac{1}{3}:\frac{5}{9}\mathrm{and}\mathrm{C}:\mathrm{D}=\frac{5}{6}:\frac{3}{4}$, then the ratio A : B : C : D is

(A) 6 : 4 : 8 : 10 (B) 6 : 8 : 9 : 10

(C) 8 : 6 : 10 : 9 (D) 4 : 6 : 8 : 10

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

Choose the right answer

PQRS is a parallelogram. The angle bisector of angle P and angle S meet at O. The measure of angle POS is

A. 45

B. 90

C. 105

D. 60

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

if the dagonal of a quadilateral bisect the opposite angle,then it isa-------?

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

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.

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

ABCD is a rectangle,with angleBAC=42.

determine angle DBC.

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.

M and N divide the side of AB of triangle ABC into 3 equal parts. Line segments MP and NQ are both parallel to BC and meets at AC at P and Q respectively. Prove P and Q divide AC into 3 equal parts.

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

ABCD is a trapezium in which AB//DC. If angle A = 55 desgree and angle B = 70 degree find angle C and angle D

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.

Prove that the figure obtained by joining the midpoints of the sides of a rhombus, taken in order, is a square.

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

In a triangle ABC, angle A=40

^{o,}, angle B=80^{o}, angle C=60^{o}. Find the measures of the angles of the angles of the triangles formed by joining the midpoints of this triangle.Please answer fast my worksheet is due on monday!!PQRS is a parallelogram in which PQ is produced to T such that QT=PQ. prove that ST bisects RQ.

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

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

Prove that angle P+ angle Q= 2angle RTS