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Syllabus

1. InΔPQR, given that S is a point on PQ such that STIIQR and PS/SQ=3/5 If PR = 5.6 cm, then find PT.

2. InΔABC, AE is the external bisector of <A, meeting BC produced at E. If AB = 10 cm, AC = 6 cm and BC = 12 cm, then find CE.

3. P and Q are points on sides AB and AC respectively, ofΔABC. If AP = 3 cm,PB = 6 cm, AQ = 5 cm and QC = 10 cm, show that BC = 3 PQ.

4. The image of a tree on the film of a camera is of length 35 mm,the distancefrom the lens to the film is 42 mm andthe distancefrom the lens to the tree is 6 m. How tall is the portion of the tree being photographed?

5. D is the midpoint of the side BC ofΔABC. If P and Q are points on AB and on AC such that DP bisects <BDA and DQ bisects <ADC, then prove that PQ II BC.

6. If a straight line is drawn parallel to one side of a triangle intersecting the othertwo sides, then it divides thetwo sidesin the same ratio.

7. If a straight line divides anytwo sidesof a triangle in the same ratio, then the line must be parallel to the third side.

8. ABCD is a quadrilateral with AB =AD. If AE and AF are internal bisectors of <BAC and <DAC respectively, then prove that EF II BD. In aΔABC, D and E are points on AB and AC respectively such that AD/ DB = AEC/EC and <ADE = <DEA. Prove thatΔABC is isosceles.

9. In aΔABC, points D, E and F are taken on the sides AB, BC and CA respectively such that DE IIAC and FE II AB.

10. The internal bisector of <A ofΔABC meets BC at D and the external bisector of <A meets BC produced at E. Prove that BD/ BE = CD/CE

11. If a perpendicular is drawn from the vertex of a right angled triangle to its hypotenuse, then the triangles on each side of the perpendicular are similar to the whole triangle.

12. A man sees the top of a tower in a mirror which is at a distance of 87.6 m from the tower. The mirror is on the ground, facing upward. The man is 0.4 maway fromthe mirror, andthe distanceof his eye level from the ground is 1.5 m. How tall is the tower? (The foot of man, the mirror and the foot of the tower lie along a straight line).

13. In a rightΔABC, right angled at C, P and Q are points of the sides CA and CB respectively, which divide these sides in the ratio 2: 1. Prove that

(I) 9AQ

^{2}= 9AC^{2}+4BC^{2 }(II) 9 BP^{2}= 9 BC^{2}+ 4AC^{2}(III) 9 (AQ^{2}+BP^{2}) = 13AB^{2}14. ABC is a triangle. PQ is the line segment intersecting AB in P and AC in Q such that PQ parallel to BC and dividesΔABC into two parts equal in area. Find BP: AB.

15. P and Q are the mid points on the sides CA and CB respectively of triangle ABC right angled at C. Prove that4(AQ

^{2}+BP^{2}) = 5 AB^{2}16. In an equilateralΔABC, the side BC is trisected at D. Prove that 9AD2 = 7AB2

17. Prove that three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians ofthe triangle.

18. If ABC is an obtuse angled triangle, obtuse angled at B and if AD^CB Prove that

1.AC

^{2}=AB^{2}+ BC^{2}+2 BC x BD19. Prove that in any triangle the sum of the squares of anytwo sidesis equal to twice the square of half of the third side together with twice the square of the median, which bisects the third side.

[To prove AB

^{2}+ AC^{2}= 2AD^{2}+ 2(1/2BC)^{2}]20. ABC is a right triangle right-angled at C and AC= √3 BC. Prove that <ABC=60

^{o}Let ABC be triangle and D and E be two pobcints on side AB such that AD=BE. if DP||BC and EQ||AC, then prove PQ||AB

What are real life applications of Thales Theorem?

in triangle ABC,if AD is perpendicular to BCand AD*2=BD.DC,prove that angle BAC=90 degree

^{2}+ ZE^{2}=5 DE^{2}.Proof of the theorem: ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

walking away from the base of a lamp post at a speed of 1 m/s. Lamp is 4.5 m above the ground.

(i) If after 2 second, length of shadow is 1 meter,

what is the height of Rohan ?

(a) 145 cm (b) 120 cm

(c) 150 cm (d) 175 cm

(ii) What is the minimum time after which his shadow

will become larger than his original height?

(a) 1 sec (b) 2 sec

(c) 3 sec (d) 4 sec

(iii) What is the distance of Rohan from pole at this

point ?

(a) 2 m (b) 1 m

(c) 3 m (d) 4 m

(iv) What will be the length of his shadow after 4

seconds?

(a) 2 m (b) 1 m

(c) 3 m (d) 4 m

(v) Which similarity criterion is used in solving the

above problem

(a) SAS similarity criterion

(b) AA similarity criterion

(c) SSS similarity criterion

(d) none of these

through the midpoint m of the side cd of a paralelogram abcd,the line bm is drawn intersecting ac in l and ad produced in e.prove that el=2bl

Prove that the ratio of areas of two similar triangles is equal to the square of their corresponding sides.

If two Triangles are equilateral then prove that the ratio of their respective sides,medians,angle bisectors and altitudes are equal.

ABC is a right triangle, right angled at C. Let BC=a, CA=b, AB=c and let p be length of perpendicular from C on AB. Prove that

(i) cp=ab

(ii) 1/p

^{2}=1/a^{2}+1/b^{2}answer as quick as possible, tomorrow is my SA- 1 exam.

in the figure of triangle ABC,d divides ca in the ratio of 4:3 .if DE// BC,then find the area of BCDE:are of triangle ABC.(diagram is not provided)

prove that in a right triangle the square of the hypotenuse is equal to the aum of the squares of the other two sides

In a triangle ABC, D and E are points on sides AB and AC respectively , such that DE is parallel to BC.If AD = 2.4cm, AE= 3.2cm , DE = 2cm and BC = 5cm , find BD and CE.

In a trapezium ABCD, AB is parallel to DC and DC = 2AB E is point on BC such that BE : EC = 3:4. EF is drawn parallel to AB where F is a point on AD . Prove that 7EF = 10AB.

A triangle has side 2, 3, 4. A tangent is drawn to the incircle parallel to side 2 cutting other two sides at X and Y. Find the length of XY

triangle ABC is right angled triangle at B.side BC is trisected at points D and E.Prove that 8AE

^{2}=3AC^{2}+5AD^{2}in a right triangle ABC , right angled at C; P and Q are points of the sides AC and BC respectively , which divides these sides in the ratio 2:1. prove that :

(a)9(AO)2=9(AC)2 + 4(BC)2

(b)9(BP)2 =9(BC)2 + 4(AC)2

(c)9[(AO)2 + (BP)2] = 13(AB)2

In triangle ABC points P,Q and R lie on sides BC, CA and AB respectively. If PQ||AB and QR||BC then prove that RP||CA

in an equilateral triangle ABC, D is a point on side BC such that BD = 1/3 BC. prove that 9 AD

^{2 }= 7 AB^{2}If O is any point inside a rectangle ABCD, then prove that OA

^{2}+ OC^{2}= OB^{2}+ OD^{2}(A) AB.AD = AE.AC (B) AB.AC = AE.AD (C) AB.AE = AC.AD (D) none of these

Prove that the sum of squares of a sides of a rhombus is equal to the sum of the squares of its diagonals......pls give answer.....u'll surely get a ''thumbs up''

Triangle PQR~ Triangle XYZ If PQ=4cm,QR=5cmand XY=6cm. Then find YZ.

In a triangle ABC, AB=AC. D is any point on BC. Show that AB

^{2}-AD^{}^{2}^{}=^{BD.CD}1. Show that the area of a rhombus on hypotenuse of a right angled triangle, with one of the angles as 60 is equal to the sum of areas of rhombuses with one of their angles as 60 drawn on others sides.

2. BO and CO bisect angle B and angle C of triangle ABC. AO produced meets BC at P. Show:-

· AB*OP=BP*AO

· AC*OP=CP*AO

· AB*PC=AC*BP

· AP bisects angle BAC.

in triangle ABC,PQ is a line segment intersecting AB at P and AC at Q such that PQllBC and PQ divides triangle ABC into two parts in equal area.Find BP/AB.

side ab and ac and median ad of a triangle abc r respectively proportional to sides pq and pr and median pm of another triangle pqr prove that triangle abc similar to pqr explain step by step it plz

Two poles of height "a" m. and "b"m. are "p" m apart. Proove that the point of intersection of lines joining the tops of the poles to bottom of the opp. poles is given by :- h = (a * b) / (a+b) m

PLZ. ANSWER EVEN A WEEK PASSED BUT NO ANS. FROM MERITNATION

ABC & BDE R THE 2 EQUILATERAL TRIANGLES SUCH THAT D IS THE MID POINT OF BC .RATIO OF THE AREAS OF TRIANGLES ABC & BDE

If BL and CM are medians of a triangle ABC right angled at A, then prove that 4( BL

^{2}+ CM^{2}) = 5 BC^{2}In a quadrilateral ABCD ,AB=DC and AB is parallel to DC . A line segment is drawn joining B and F a point on AD produced .If the point of intersection of BF and CD is E and ar of AED =7 cm^2 , Find the area of triangle CEF.

In triangle ABC, DE is parallel to BC and AD:DB=5:4. diagonals DC and BE intersect at F. Find Area(triangle DEF) / Area(triangle CFB).

In triangle ABC, AD is a median . Prove that AB

^{2}+ AC^{2}= 2(AD^{2}+ BD^{2})drawing boundaries PQ and RS which are parallel to BC.

Other measurements are as shown in the figure.

i. What is the area of this land?

ii. What is the length of PQ?

iii. The length of RS is

iv. Area of? APQ is?

v. What is the area of? ARS?

In a quadrilateral ABCD, Angle B=90 degree, AD

^{2}=AB^{2}+BC^{2}+CD^{2}.Prove that Angle ACD=90 degree.

The side BC of an equilateral triangle ABC is extended to D such that BC =CD. Prove that AD

^{2}=3AC^{2.}prove that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides

drawing boundaries PQ and RS which are parallel to BC.

Other measurements are as shown in the figure.

i. What is the area of this land?

ii. What is the length of PQ?

iii. The length of RS is

iv. Area of? APQ is?

v. What is the area of? ARS?

If A be the area of a right triangle and b one of the sides containing the right angle, the length of the altitude on the hypotenuse is__________.

a) 2A/√(b

^{2}+2A^{2}) b) 2Ab/√(b^{4}+4A^{2}) c)2Ab^{2}/√(b^{3}+4A^{2}) d)2A^{2}b/√(b^{4}+3A^{2})In triangle ABC if AD is the median then show that AB

^{2}+ AC^{2}= 2(AD^{2}+ BD^{2})D is the midpoint of side BC of a triangle ABC.AD is bisected at a point E and BE produced cuts AC at the point X.Prove that - BE : EX = 3:1

Q.1- ABC is a right triangle, right angled at C. If p is the length of the perpendicular from C to AB & AB=c, BC=a & AC=b. Prove that (i)pc=ab, (ii)1/p

^{2}=1/a^{2}+1/b^{2}.Q.2- PRQ is a right triangle, right angled at Q. S & T are points on QR such that QS=ST=TR. Prove that 8PT

^{2}=3PR^{2}+5PS^{2}.Q.3- AD is the bisector of angle BAC of triangle ABC. The length of BC=a, AC=b & AB=c. Prove that BD=ac/b+c, CD=ab/b+c.

Q.4-

ABCDis a parallelogram. DM=CM. Prove that EL=2BL.Q.5- IN triangle ABC, XYllBC & it divides triangle ABC into two parts of equal area. Find BX/AB.

Q.6- If A is the area of a right angled triangle & 'b' is one of the sides containing right angle. Prove thet the length of altitude on the hypotenuse is 2Ab/(under root)b

^{4}+4A^{2.}In triangle ABC, angle A=60. Prove that BC

^{2}=AB^{2}+AC^{2}- AB.ACAD is the median of triangle ABC .The bisector of angle ADB and angle ADC meet AB and AC at E F resp.Prove that EF parallel BC

Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.

If the diagonals of a quadrilateral divide each other proportionally , prove that itAskis a trapezium

IN THE GIVEN FIGURE, DB IS PERPENDICULAR TO BC, DE IS PERPENDICULAR TO AB AND AC IS PERPENDICULAR TO BC. PROVE THAT BE/DE= AC/BC.1.Show that the area of a rhombus on hypotenuse of a right angled triangle, with one of the angles as 60 is equal to the sum of areas of rhombuses with one of their angles as 60 drawn on others sides.

2.BO and CO bisect angle B and angle C of triangle ABC. AO produced meets BC at P. Show:-

�AB*OP=BP*AO

�AC*OP=CP*AO

�AB*PC=AC*BP

�AP bisects angle BAC.

i am a meritnation paid user

in equilateral trangle d is a pnt on bc side bd=1third bc prove that 9ad2 =7ab2

In the given figure ABCD is parallelogram in which DC=10cm and BC=4root3cm. AP is perpendicular to DC. If angle ADC = 60. Find:(i) length of AP

(ii) Area of parallelogram ABCD

if AD is perpendicular to BC and BD=1/3 CD.prove that 2AC

^{2}=2AB^{2}+BC^{2}what is the difference between - median , altitude , perpendicular bisector and perpendicular - in a triangle?

please explain

In triangle ABC , AD is perpendicular to BC. Prove that AD

^{2}= 3DC....tried the question many tyms...cn sum1 pls explain with the steps.thankyou...

In a triangle ABC , AB =AC and D is a point on side AC , such that BC2=AC.CD . Prove that BD =BC . PLEASE HELP ME MERITNATION !!!

TO BE ANSWERED BY EXPERTS ONLY!!!in triangle pqr

PQ = 4.2 cm

PR = 3 root 3 cm

QR = 7 cm

angle p = 60 degree

angle q = 70 degree

in triangle xyz

XZ = 6 root 3 cm

XY = 14 cm

ZY = 8.4 cm

find the value of angle x

What are various aspects of pythagoras theorem?

3. पोस्ट ऑफिस में दिव्यांश तथा बाबू के बीच

निर्देशः दिव्यांश के पिता उसे स्पीड पोस्ट करने के लिए पोस्ट ऑफिस में भेजते है। दिव्यांश तथा बाबू के बीच हुई इस बातचीत को संवाद के रूप में लिखिए।

x+1/y= 1/zand walked 5 km. Then he turned west and walked 4 km. Finally he turned left and walked 12 km. Then

40. How far Ajit is from his original place ?

(1) 13 km (2) 17 km (3) 18 km (4) 7 km. In this question can you please explain why after walking 5km southeast Ajit will be on a line on which A lies ? Can't he be below the line ?

In an equilateral triangle ABC,D is a point on side BC such that 4BD = BC. prove that 16AD

^{2}= 13BC^{2}In the figure - PA,, QB and RC are perpendiculars to AC. prove that 1/x + 1/z = 1/y

In the following figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that

(i) AB

^{2}= BC × BD(ii) AC

^{2}= BC × DC(iii) AD

^{2}= BD × CDhow to do this using pythagoras theorem ?

n RD Sharma 's Maths page 4.3,Q.2(vi) state T/F for the statement All Triangles with proportionate angles are similar, the answer shown by you is TRUE. Please clarify the correctness of the answer.

Radha(parent)

D is a point on the side BC of triangle ABC such that angle BAC= angle ADC. Prove that CA

^{2}= CB x CDA child 1.2 meters tall is standing 11 meters away from atall buliding. A spotlight on the ground is located 20 meters away from the buliding and shines on the wall. How tall is the child's shadow on the buliding?

In given figure, is a right triangle PQR, right angled at Q. X and Y are the points on PQ and QR such that PX : XQ=

1 : 2 and QY : YR= 2 : 1. Prove that 9(PY2+XR2)=13PR2.In triangle ABC, P and Q are points on the sides AB and AC respectively such that PQ is parallel to BC. Prove that medium AD, drawn from A to BC, bisects PQ.

Please explain the exterior angle bisector theorem!!!

A vertical pole which is 2.25 m long casts a 6.75 m long shadow on the ground. At the same time , a vertical tower casts a 90 m long shadow on the ground .Find the height of the tower.

In the adjoining figure, ABCD is a trapezium in which CD||AB and its diagonals intersect at O. If AO=(5x-7)cm, OC=(2x+1)cm, DO=(7x-5)cm and OB=(7x+1)cm, find the value of x.

Experts, this question is from RS Aggarwal book (Class 10 Mathematics) and the same question's solution is also given on your website. But the values of OB and OD have been interchanged in your solution so the answer is coming right. But is that the correct way to do this question?? Please give the correct solution. Please answer fast, have to give an assignment tomorrow...

In a quadrilateral ABCD, AB = CD and AB is parallel to CD. A line segment is drawn joining B and F, a point on AD produced. If the point of intersection of BF and CD is E and area of triangle AED = 7cm

^{2}, then what is the area of triangle CEF?SAMPLE PAPER/MODEL TEST PAPERSUBJECT – MATH 10^{TH}CBSE SA 2 2011Section – A1. A number is selected from numbers 1 to 25. The probability that it is prime is:

(a) 5/6(b) 1/3(c) 1/6(d) 2/3

2. If the angle of elevation of the top of a tower from two points distance a and b from the base and in the same straight line with at are complementary, then the height of the tower is:

(a) a/b(b) ab(c) √ ab(d) √a/b

3. The perimeter of a triangle is 30 cm and the circumference of its in circle is 88 cm. Then area of triangle is:

(a) 420 cm

^{2}(b) 140 cm^{2}(c) 70 cm^{2}(d) 210 cm^{2}4. If the first term of an A.P. is 2 and common difference is 4, then the sum of its 40 terms is:

(a) 2800(b) 16000(c) 3200(d) 200

5. The surface area of a sphere is same as the curved surface of right circular cylinder whose height and diameter are 12 cm each. The radius of the sphere is:

(a)12 cm(b) 4 cm(c) 3 cm(d) 6 cm

6. If the circumference and the area of a circle are numerically equal, then diameter of the circle is:

(a) π/2(b) 2π(c) 2(d) 4

7. AB and CD are two common tangents of circles which touch each other at C. If D lies on AB such that CD = 4 cm, then AB is equal to:

(a)12cm(b) 6 cm(c) 4 cm(d) 8cm

8. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q such that OQ= 12 cm. Length PQ is:

(a) 13 cm (b) 8.5 cm(c) √119(d) 12 cm

9. If three coins are tossed simultaneously, then the probability of getting at least two heads, is:

(a) ¼(b) ½(c) 2/4 (d) 3/8

10. The area of in circle of an equilateral triangle is 154 cm

^{2}.The perimeter of the triangle is:(a) 72.7 cm(b) 72.3 cm(c) 71.5 cm(d)71.7 cm

Section – B11. Prove that the tangents drawn at the ends of a diameter of a circle are paralled.

12.A bag contains 7 white, 4 red and 9 black balls. A ball is drawn at the random. What is the probability that ball drawn is not white?

13. Shoe that the points (7, 10), (-2, 5) and (3, -4) are the vertices of an isosceles right triangle.

14. Using the quadratic formula, solve the equation:

A

^{2}b^{2}x^{2}– (4b^{4}– 3a^{4}) x – 12a^{2}b^{2}= 015. Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

16. Find the radius of circle whose area is equal to the sum of the areas of three circles whose radii are 3 cm, 4 cm and 12cm.

17. The line segment joining the points (3, -4) and (1, 2) is trisected at the points P and Q.

If the coordinates of P and Q are (p, -2) and (5/3, q) respectively, find the values of p and q.

18. Find the area of a circular ring whose external and internal diameters are 20 cm and 6 cm.

Section – C19. If m times the m

^{th}tern of an A.P. is equal to n times its n^{th}term, find (m + n)^{th}term of A.P.?20.Two tangents TP and TQ are drawn from an external point T to a circle with centre O. As shown in fig. or if they are inclined to each other at an angle of 100

^{0}then what is the value of ∟POQ?21. From the top of house, h meters high from the ground, the angle of elevation and depression of the top and bottom of a tower on the other side of the street are ѳ and φ, respectively. Prove that the height of the tower h (1+ tan ѳ cot ѳ).

22. A motor boat whose speed is 8cm/hour in still water goes 15 km down stream and comes back in a total time of 3 hours 40 minutes. Find the speed of the stream.

23. For what value of n are the nth terms of two A.P. is 63, 65, 67 ……… and 3, 10, 17……… equal?

24. Construct a triangle ABC in which AB = 6.5 cm, ∟B = 60

^{0}and BC = 5.5 cm. Also construct a triangle ABC similar to triangle ABC, whose each side is 3/2 times the corresponding side of the triangle ABC.25. A bag contains 5 white balls, 7 red balls, 4 black balls and 2blue balls. One ball is drawn at random from the bag. What is the probability that the ball drawn is:

(a) Not white

(b) Red or black

(c) White or blue

(d) Neither white not black

26. PQRS is a square land of the side 28 m. Two semicircular grass covered portions are to be made on two of its opposite sides as shown in the figure. How much area will be left uncovered? [Take π = 22/7]

27. A solid composed of a cylinder with hemispherical ends. If the whole length of the solid is 104 cm and radius of each hemispherical end is 7cm, find the cost of polishing its surface at the rate of Rs.10 per dm

^{2}28. If A (4,-8), B (3, 6) and C (5, -4) are the vertices of triangle ABC, D is the mid point of BC and P is a point on adjoined such that AP/PD = 2. Find the coordinate of P.

Section – D29. Solve for x:

X

^{4}+2x^{3}+ 13x^{2}+ 2x + 1 = 0.30. The angles of depression of the top and bottom of an8 m tall building from the top of a multistoreyed building are 30

^{0}and 45^{0}respectively. Find the height of the multi storeyed building and the distance between the two buildings.31. Solve for x:

2 (x

^{2}+ 1/x^{2}) – (x + 1/x) – 11 = 032. A class consists of a number of boys whose ages are in A.P., the common difference being 4 months. If they youngest boy is just eight years old and if sum of the ages is 168 years. Find the number of boys in the class.

33. Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 7/5 of the corresponding sides of first triangle.

34. A car has to wipers which do not over lap each wiper has a blade of length 25 cm sweeping through an angle 115

^{0 }. Find the total area cleared at each sweep of the blades.Two poles of height a and b metres are p metre apart . Prove that the height of each pole to the foot of opposite pole is given by ab/a+b metres.

1. In triagleABC DE ll BC and AD = 1/3AB. Find ar[ADE]/ar[DBCE]

ABC and DBC are two triangles on the same base BC.If AD intersects BC at O,show that ar(ABC)/ar(DBC)=AO/DO

A) AB/BC = AE/ED

B) AB.AC = AE.ED

C) AB^2 = AC^2

D) None of these

IF THE AREAS OF TWO SIMILAR TRIANGLES ARE EQUAL,,PROVE THAT THEY ARE CONGRUENT...

$\left(1\right)100\xb0\left(2\right)65\xb0\left(3\right)130\xb0\left(4\right)\mathrm{None}\mathrm{of}\mathrm{these}.$