CLASS 10 MATH NCERT SOLUTIONS FOR CHAPTER – 6 TRIANGLES EX – 6.3

Triangles

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 :
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 20
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 21

Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 22
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 23
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 24

Question 2.
In the given figure, ∆ODC ~ ∆OBA, ∠BOC = 125° and ∠CDO = 70°. Find ∠DOC, ∠DCO and ∠OAB.

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 25


Solution:

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 26
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 27

Question 3.
Diagonals AC and BD of a trape∠ium ABCD with AB || DC intersect each other at the point O. Using a similarity criterion for two triangles, show that 

Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 28

Question 4.
In the given figure,  and ∠1 = ∠2. show that ∆PQR ~ ∆TQR.

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 29


Solution:

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 30

Question 5.
S and T are points on sides PR and QR of ∆PQR such that ∠P = ∠RTS. Show that ∆RPQ ~ ∆RTS.

Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 31
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 32

Question 6.
In the given figure, if ∆ABE ≅ ∆ACD, show that ∆ADE ~ ∆ABC.

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 33


Solution:

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 34

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

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 35


Solution:

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 36

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:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 37

Question 9.
In the given figure, ABC and AMP are two right triangles, right angled at B and M respectively. Prove that:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 38

Solution:

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 39

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

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 40

Solution:

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 41
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 42

Question 11.
In the given 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.

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 43


Solution:

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 44

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.

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 45


Solution:

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 46
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 47
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 48

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

Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 49
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 50

Question 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 ∆ABC ~ ∆PQR.

Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 51

Question 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.

Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 52

Question 16.
If AD and PM are medians of triangles ABC and PQR respectively, where
∆ABC ~ ∆PQR. Prove that 

Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 53
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 54

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