NCERT Class 10 Maths Triangles Chapter Problem Solutions & Video Lessons
#1
Watch the below videos to get the complete basic principles and textbook problem solutions of TRIANGLES Chapter in NCERT CBSE STD X Mathematics Textbook.

Video classes are taken and solutions are discussed by Smt. Radhika Polina.

This class will help you to learn all the basic concepts in the chapter TRIANGLES.. like

SIMILAR TRIANGLES
BASIC PROPORTIONALITY THEOREM
CONVERSE OF BASIC PROPORTIONALITY THEOREM


Triangles | Part-1| Class 10|  Introduction to the chapter & Exercise-2.1

Exercise 2.1 is discussed in this class

1. Fill in the blanks using the correct word given in brackets :
(i) All circles are ........... (congruent, similar)
(ii) All squares are ............. (similar, congruent)
(iii) All  triangles are similar. .............(isosceles, equilateral)
(iv) Two polygons of the same number of sides are similar, if (a) their corresponding angles are  and (b) their corresponding sides are .(equal, proportional)

2. Give two different examples of pair of (i) similar figures. (ii) non-similar figures.

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#2
Triangles | Part-2| Class 10|Basic proportionality theorem,converse
Solutions for class 10th mathematics NCERT/CBSE syllabus
This video explains the Basic Proportionality theorem (The ratio of any two corresponding sides in two equiangular triangles is always the same.),Converse,corollary(1,2,3) in easy method.


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#3
Triangles | Part-3| Class 10|Exercise-2.2|Problems(1&2)

In this video teacher explains the solutions for the following textbook problems.

1. In Fig. 6.17, (i) and (ii), DE || BC. Find EC in (i) and AD in (ii).

2. E and F are points on the sides PQ and PR respectively of a Δ PQR. For each of the following cases, state whether EF || QR :
(i) PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm
(ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm
(iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36cm


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#4
NCERT Class 10 Maths Chapter- Triangles | Part-4| Class 10|Exercise-2.2|Problems(3-6)

This class explains the below problems:

3. In Fig. 6.18, if  LM || CB and LN || CD, prove that AM /MN= AB/ BD.

4. In Fig. 6.19, DE || AC and DF || AE. Prove that BF/ BE= FE/ EC .

5. In Fig. 6.20, DE || OQ and DF || OR. Show that EF || QR. 

6. In Fig. 6.21, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

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#5
NCERT Class 10 Maths Chapter- Triangles  | Part-5| Class 10|Exercise-2.2|Problems(3,7-10)


In this video teacher explains solutions to the below problems:

3. In Fig. 6.18, if  LM || CB and LN || CD, prove that AM/ AN =AB/ AD .

7. Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX).

8. Using Theorem 6.2, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side. (Recall that you have done it in Class IX).

9. ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show  that  AO CO BO DO =⋅ 

10. The diagonals of a quadrilateral ABCD intersect each other at the point O such that AO CO BO DO =â‹… Show that ABCD is a trapezium.

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#6
NCERT Class 10 Maths Video Lessons
Chapter- Triangles  | Part-6| Class 10|Theorems 2.3,2.4 & 2.5


solutions for class 10th mathematics NCERT/CBSE syllabus

This video explains Theorems (2.3,2.4& 2.5) in NCERT/CBSE Maths textbook.

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#7
NCERT Class 10 Maths Video Lessons
Triangles | Part-7| Class 10|Exercise-6.3|Problems(1,2 & 3 )

In this video teacher explains solutions to the following problems

Exercise 6.3.1 (i-vi)
State which pairs of triangles in Fig. 6.34 are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form :


Exercise 6.3.2
In Fig. 6.35, ∆ ODC ~ ∆ OBA, ∠ BOC = 125° and ∠ CDO = 70°. Find ∠ DOC, ∠ DCO and ∠ OAB.

Exercise 6.3.3
Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Using a similarity criterion for two triangles, show that OA/ OB = OC /OD

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#8
NCERT Class 10 Maths Video Lessons

Triangles | Part-8| Class 11|Exercise 6.3 Problems -14, 15 and 16

In this video teacher explains solutions to the following problems

14. Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that Δ ABC ~ Δ PQR.

15. A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

16. If AD and PM are medians of triangles ABC and PQR, respectively where
Δ ABC ~ Δ PQR, prove that
AB /AD= PQ/ PM


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#9
NCERT Class 10 Maths Video Lessons

Triangles | Part-9| Class 10|Exercise-2.3|Problems(8,9 & 10)

This video explains the below problems:

8. E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that Δ ABE ~ Δ CFB.


9. In Fig. 6.39, ABC and AMP are two right triangles, right angled at B and M respectively. Prove that:
(i) Δ ABC ~ Δ AMP
(ii)CA/ BC= PA/ MP 


10. CD and GH are respectively the bisectors of ∠ ACB and ∠ EGF such that D and H lie on sides AB and FE of Δ ABC and Δ EFG respectively. If Δ ABC ~ Δ FEG, show that:
(i) CD /AC = GH/ FG
(ii) Δ DCB ~ Δ HGE
(iii) Δ DCA ~ Δ HGF


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#10
NCERT Class 10 Maths Video Lessons

Triangles | Part-10| Class 10|Exercise-2.3|Problems(11,12 & 13)


This video explains the below problems:

11. In Fig. 6.40, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC, prove that Δ ABD ~ Δ ECF.

12. Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of Δ PQR (see Fig. 6.41). Show that Δ ABC ~ Δ PQR.

13. D is a point on the side BC of a triangle ABC such that ∠ ADC = ∠ BAC. Show that CA2 = CB.CD. 

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#11
Triangles | Part-11| Class 10|Exercise-2.3|Problems(14,15 & 16)

This video explains the below problems:

14. Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that Δ ABC ~ Δ PQR. 

15. A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower. 

16. If AD and PM are medians of triangles ABC and PQR, respectively where
Δ ABC ~ Δ PQR, prove that
AB /AD= PQ/ PM


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#12
Triangles | Part-12| Class 10|Theorem 6.6|Exercise-6.4|Problems(1 &2)

This video explains the below problems:

1. Let Δ ABC ~ Δ DEF and their areas be, respectively, 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC. 


2. Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2 CD, find the ratio of the areas of triangles AOB and COD.

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#13
Triangles | Part-13| Class 10|Exercise-6.4|Problems(3,4 &5)

This video explains the below problems:
*********************************************************
3. In Fig. 6.44, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that ar (ABC) AO= ar (DBC) DO â‹…

4. If the areas of two similar triangles are equal, prove that they are congruent.

5. D, E and F are respectively the mid-points of sides AB, BC and CA of Δ ABC. Find the ratio of the areas of Δ DEF and Δ ABC.

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#14
Triangles | Part-14| Class 10|Exercise-6.4|Problems(6,7,8 &9)

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

7. 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. 

Tick the correct answer and justify :
8. ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is (A) 2 : 1 (B) 1 : 2 © 4 : 1 (D) 1 : 4 


9. Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio (A) 2 : 3 (B) 4 : 9 © 81 : 16 (D) 16 : 81

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#15
Triangles | Part-15| Pythagoras theorem & its Converse,Pythagoras triplet

This class deals with Pythagoras theorem & its Converse,Pythagoras triplet in Chapter Trianngles of NCERT STD 10 Maths textbook.

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