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NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.3

NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.3 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.3.

  • Triangles Class 10 Ex 6.1
  • Triangles Class 10 Ex 6.2
  • Triangles Class 10 Ex 6.3
  • Triangles Class 10 Ex 6.4
  • Triangles Class 10 Ex 6.5
  • Triangles Class 10 Ex 6.6
Board CBSE
Textbook NCERT
Class Class 10
Subject Maths
Chapter Chapter 6
Chapter Name Triangles
Exercise Ex 6.3
Number of Questions Solved 16
Category NCERT Solutions

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 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 :
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

Ex 6.3 Class 10 Maths 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

Ex 6.3 Class 10 Maths 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 \(\frac { OA }{ OC } =\frac { OB }{ OD^{ \bullet } } \)
Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 28

Ex 6.3 Class 10 Maths Question 4.
In the given figure, \(\frac { QR }{ QS } =\frac { QT }{ PR } \) 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

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

Ex 6.3 Class 10 Maths 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

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
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 35
Solution:

NCERT Solutions for Class 10 Maths Chapter 6 Triangles 36

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:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 37

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:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 38
Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 39

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
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

Ex 6.3 Class 10 Maths 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

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.
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

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

Ex 6.3 Class 10 Maths 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

Ex 6.3 Class 10 Maths 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

Ex 6.3 Class 10 Maths Question 16.
If AD and PM are medians of triangles ABC and PQR respectively, where
∆ABC ~ ∆PQR. Prove that \(\frac { AB }{ PQ } =\frac { AD }{ P{ M }^{ \bullet } } \)
Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 53
NCERT Solutions for Class 10 Maths Chapter 6 Triangles 54

 

We hope the NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.3 help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.3, drop a comment below and we will get back to you at the earliest.

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