Chapter 6 Triangles Ex 6.3

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 Ex 6.1 Q7

NCERT Solutions For Class 10 Maths Chapter 6 Triangles Ex 6.1 Q8
Solution:
ncert solutions for class 10 maths chapter 6 triangles
ncert solutions for class 10 maths chapter 6 pdf

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 Ex 6.1 Q9
Solution:
ncert solutions for class 10 maths triangles

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 OAOC=OBOD
Solution:
triangles class 10 solutions

Question 4.
In the given figure, QRQS=QTPR and ∠1 = ∠2. show that ∆PQR ~ ∆TQR.
NCERT Solutions For Class 10 Maths Chapter 6 Triangles Ex 6.1 Q10
Solution:
similarity of triangles class 10

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 Exercise 6.3 Triangles in English medium PDF

Question 6.
In the given figure, if ∆ABE ≅ ∆ACD, show that ∆ADE ~ ∆ABC.
NCERT Solutions For Class 10 Maths Chapter 6 Triangles Ex 6.1 Q11
Solution:
NCERT Solutions for Class 10 Maths Chapter 6 Exercise 6.3 Tribhuj in Hindi medium PDF

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 Ex 6.1 Q12
Solution:
Triangles Class 10 Ex 6.3

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:
Triangles Class 10 Exercise 6.3

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 Ex 6.1 Q13
Solution:
exercise 6.3 class 10

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 Ex 6.1 Q14
Solution:
class 10 maths triangles ex 6.3
exercise 6.3 class 10 ncert solutions

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 Ex 6.1 Q15
Solution:
Class 10 Triangles Exercise 6.3

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 Ex 6.1 Q16
Solution:
Chapter 6 Maths Class 10 Ex 6.3 NCERT Solutions PDF

Question 13.
D is a point on the side BC of a triangle ABC, such that ∠ADC = ∠BAC. Show that CA² = CB.CD.
Solution:
similar triangles class 10 ex 6.3

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:
chapter 6 maths class 10 ex 6.3

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:
class 10 maths chapter 6 ex 6.3

Question 16.
If AD and PM are medians of triangles ABC and PQR respectively, where
∆ABC ~ ∆PQR. Prove that ABPQ=ADPM
Solution:
ncert solutions for class 10 maths chapter 6 triangles ex 6.3