**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 :

**Solution for Ex 6.3 Class 10 Maths Question 1**

**Solution for Ex 6.3 Class 10 Maths Question 1**

**Ex 6.3 Class 10 Maths Question 2.**

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

**Solution for Ex 6.3 Class 10 Maths Question 2**

**Solution for Ex 6.3 Class 10 Maths Question 2**

**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

**Solution for Ex 6.3 Class 10 Maths Question 3**

**Solution for Ex 6.3 Class 10 Maths Question 3**

**Ex 6.3 Class 10 Maths Question 4.**

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

**Solution for Ex 6.3 Class 10 Maths Question 4**

**Solution for Ex 6.3 Class 10 Maths Question 4**

**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 for Ex 6.3 Class 10 Maths Question 5**

**Solution for Ex 6.3 Class 10 Maths Question 5**

**Ex 6.3 Class 10 Maths Question 6.**

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

**Solution for Ex 6.3 Class 10 Maths Question 6**

**Solution for Ex 6.3 Class 10 Maths Question 6**

**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

**Solution for Ex 6.3 Class 10 Maths Question 7**

**Solution for Ex 6.3 Class 10 Maths Question 7**

**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 for Ex 6.3 Class 10 Maths Question 8**

**Solution for Ex 6.3 Class 10 Maths Question 8**

**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:

**Solution for Ex 6.3 Class 10 Maths Question 9**

**Solution for Ex 6.3 Class 10 Maths Question 9**

**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

**Solution for Ex 6.3 Class 10 Maths Question 10**

**Solution for Ex 6.3 Class 10 Maths Question 10**

**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.

**Solution for Ex 6.3 Class 10 Maths Question 11**

**Solution for Ex 6.3 Class 10 Maths Question 11**

**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.

**Solution for Ex 6.3 Class 10 Maths Question 12**

**Solution for Ex 6.3 Class 10 Maths Question 12**

**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 for Ex 6.3 Class 10 Maths Question 13**

**Solution for Ex 6.3 Class 10 Maths Question 13**

**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 for Ex 6.3 Class 10 Maths Question 14**

**Solution for Ex 6.3 Class 10 Maths Question 14**

**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 for Ex 6.3 Class 10 Maths Question 15**

**Solution for Ex 6.3 Class 10 Maths Question 15**

**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

**Solution for Ex 6.3 Class 10 Maths Question 16**

**Solution for Ex 6.3 Class 10 Maths Question 16**