# Triangles Class 10th Maths Ncert

We are sharing **Triangles Class 10th Maths** questions and **ncert questions for class 10th maths Triangles** to help the students appearing for class 10th board examinations with the solutions of **triangles class 10th maths** to improve their accuracy in mathematics.

Contents

## NCERT Solutions For Class 10 Maths Chapter 6 Triangles Ex 6.1

Ex 6.1 Class 10 Maths Question 1.

Fill in the blanks by 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)

Solution:

Give two different examples of pairs of

(i) similar figures.

(ii) non-similar figures.

Solution:

Ex 6.1 Class 10 Maths Question 3.

State whether the following quadrilaterals are similar or not

Ex 6.2 Class 10 Maths Question 1.

In the given figure (i) and (ii), DE || BC. Find EC in (i) and AD in (ii).

Ex 6.2 Class 10 Maths Question 2.

E and F are points on the PQ and PR sides of a ∆QPR. 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

Ex 6.2 Class 10 Maths Question 3.

The figure shows if LM || CB and LN || CD.

Ex 6.2 Class 10 Maths Question 4.

In the given figure, DE || AC and DF || AE.

Ex 6.2 Class 10 Maths Question 5.

The figure shows DE || OQ and DF || OR. Show that EF || QR.

Ex 6.2 Class 10 Maths Question 6.

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

### Triangles Class 10th Maths Ex 6.3

Ex 6.3 Class 10 Maths Question 1.

State which pairs of triangles in the given figures 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 :

Ex 6.3 Class 10 Maths Question 2.

In the given figure, ∆ODC ~ ∆OBA, ∠BOC = 125° and ∠CDO = 70°. Find ∠DOC, ∠DCO and ∠OAB.

Ex 6.3 Class 10 Maths Question 2.

In the given figure, ∆ODC ~ ∆OBA, ∠BOC = 125° and ∠CDO = 70°. Find ∠DOC, ∠DCO and ∠OAB.

Ex 6.3 Class 10 Maths Question 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 OAOC=OBOD∙

Solution:

Ex 6.3 Class 10 Maths Question 4.

In the given figure, QRQS=QTPR and ∠1 = ∠2. show that ∆PQR ~ ∆TQR.

Ex 6.3 Class 10 Maths Question 5.

S and T are points on sides PR and QR of ∆PQR such that ∠P = ∠RTS. Show that ∆RPQ ~ ∆RTS.

Solution:

Ex 6.3 Class 10 Maths Question 6.

In the given figure, if ∆ABE ≅ ∆ACD, show that ∆ADE ~ ∆ABC.

Ex 6.3 Class 10 Maths Question 7.

In the given figure, altitudes AD and CE of ∆ABC intersect each other at the point P. Show that:

(i) ∆AEP ~ ∆CDP

(ii) ∆ABD ~ ∆CBE

(iii) ∆AEP ~ ∆ADB

(iv) ∆PDC ~ ∆BEC

Ex 6.3 Class 10 Maths Question 8.

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

Solution:

Ex 6.3 Class 10 Maths Question 9.

In the given figure, ABC and AMP are two right triangles, right angled at B and M, respectively. Prove that:

Ex 6.3 Class 10 Maths Question 10.

CD and GH are, respectively, the bisectors of ∠ACB and ∠EGF such that D and H lie on sides AB and FE of ∆ABC and ∆EFG, respectively. If ∆ABC ~ ∆FEG, show that

Ex 6.3 Class 10 Maths Question 11.

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

Ex 6.3 Class 10 Maths Question 12.

Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of ∆PQR (see in given figure). Show that ∆ABC ~ ∆bPQR.

Ex 6.3 Class 10 Maths Question 13.

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

Solution

## Triangles Class 10th Maths Ex 6.4

Ex 6.4 Class 10 Maths Question 1.

Let ∆ABC ~ ∆DEF and their areas be 64 cm^{2} and 121 cm^{2}. If EF = 15.4 cm, find BC.

Solution:

Ex 6.4 Class 10 Maths Question 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.

Solution:

Ex 6.4 Class 10 Maths Question 3.

In the given figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that:

Ex 6.4 Class 10 Maths Question 5.

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

Solution:

Ex 6.4 Class 10 Maths Question 5.

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

Solution:

Ex 6.4 Class 10 Maths Question 6.

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

Solution:

Ex 6.4 Class 10 Maths Question 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.

Solution:

## Triangles Class 10th Maths Ex 6.5

Ex 6.5 Class 10 Maths Question 1.

Sides of triangles are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse.

(i) 7 cm, 24 cm, 25 cm

(ii) 3 cm, 8 cm, 6 cm

(iii) 50 cm, 80 cm, 100 cm

(iv) 13 cm, 12 cm, 5 cm

Solution:

Ex 6.5 Class 10 Maths Question 2.

PQR is a triangle right angled at P, and M is a point on QR such that PM ⊥ QR. Show that PM^{2} = QM X MR.

Solution:

Ex 6.5 Class 10 Maths Question 3.

The figure shows ABD is a triangle right angled at A and AC i. BD. Show that

(i) AB^{2} = BC.BD

(ii) AC^{2} = BC.DC

(iii) AD^{2} = BD.CD

Ex 6.5 Class 10 Maths Question 4.

ABC is an isosceles triangle right angled at C. Prove that AB^{2} = 2AC^{2}.

Solution:

Ex 6.5 Class 10 Maths Question 6.

ABC is an equilateral triangle of side la. Find each of its altitudes.

Solution:

Ex 6.5 Class 10 Maths Question 9.

A ladder 10 m long reaches a window 8 m above the ground. ind the distance of the foot of the ladder from base of the wall.

Solution:

Ex 6.5 Class 10 Maths Question 10.

A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?

Solution:

Ex 6.5 Class 10 Maths Question 16.

In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.

Solution:

## Triangles Class 10th Maths Ex 6.6

Ex 6.6 Class 10 Maths Question 2.

In the given figure, D is a point on hypotenuse AC of ∆ABC, DM ⊥ BC and DN ⊥ AB. Prove that:

(i) DM^{2} = DN X MC

(ii) DN^{2} = DM X AN

Ex 6.6 Class 10 Maths Question 3.

The figure shows ABC is a triangle in which ∠ABC > 90° and AD ⊥ CB is produced. Prove that AC^{2} = AB^{2} + BC^{2} + 2BC X BD

Ex 6.6 Class 10 Maths Question 5.

The given figure shows Ad’s median of a triangle ABC and AM ⊥ BC. Prove that

Ex 6.6 Class 10 Maths Question 6.

Prove that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.

Solution:

Ex 6.6 Class 10 Maths Question 10.

Nazima is fly fishing in a stream. The trip of her fishing rod is 1.8m above the surface of the water, and the fly at the end of the string rests on the water 3.6m away and 2.4 m from a point directly under the trip of the rod. Assuming that her string (from the trip of the rod to the fly) is that, how much string does she have out (see the figure)? If she pills in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?

## Conclusion

We have penned down the **triangles class 10th maths** solutions to help the board appearing students better understand the chapter Triangles Class 10th. We have also provided **NCERT Solutions of class 10th Triangles** to give you the solutions to improve your accuracy and depth of the chapter **Triangles Class 10th.**

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