## Chapter 1 - Similarity

## Time - 60 Minutes

## Marks - 20

## 1. All the questions are compulsory.

2. Read the question paper carefully.

3. Marks are included against each question.

**Q1. Choose the correct alternative for each of the following questions. (4 marks)**

1. The sides of two similar triangles are 4 : 9. What is the ratio of their area?

(A) 2 : 3

(B) 4 : 9

(C) 81 : 16

(D) 16 : 81

2. In ∆ABC, P is a point on side BC such that BP= 4 cm and PC = 7 cm. A (∆APC) : A (∆ABC) = ______

(A) 11 : 7

(B) 7 : 11

(C) 4 : 7

(D) 7 : 4

3. In ∆ABC, line PQ side BC, AP = 3, BP = 6, AQ = 5 then the value of CQ is _______

(A) 20

(B) 10

(C) 5

(D) 16

4. For a given one-one correspondence between the vertices of two triangles, if two angles of one triangle are congruent with the corresponding two angles of the other triangle, then the two triangles are similar.

(A) S-A-S test

(B) S-S-S test

(C) A-A test

(D) A-A-A test

#### Q2. Solve the following: (Any 3) 6 marks

1. Ratio of areas of two triangles with equal height is 2 : 3. If base of smaller triangle is 6 cm then what is the corresponding base of the bigger triangles.

2. In the figure, A – D – C and B – E – C. Seg DE || side AB. If AD = 5, DC = 3, BC = 6.4, then find BE.

3. In ∆XYZ, XY = YZ. Ray YM bisects ∠XYZ. X – M – Z. Prove that M is midpoint of seg XZ.

4. ∆DEF ~ ∆MNK, If DE = 5 and MN = 6, then find the value of A(∆DEF) : A(∆MNK).

**Q3. Solve the following: (Any 2) 6 marks**

1. D is a point on side BC of ∆ABC such that, ∠ADC ≅ ∠BAC. Show that AC² = BC × DC.

2. In the adjoining figure, seg PA, seg QB, seg RC and seg SD are ⊥ to line l. AB = 6, BC = 9, CD = 12 and PS = 36, then find PQ, QR and RS.

3. In the adjoining figure, RP : PK = 3 : 2, then find the value of

(i) A(∆TRP) : A(∆TPK)

(ii) A(∆TRK) : A(∆TPK)

(iii) A(∆TRP) : A(∆TRK)

**Q4. Solve the following: (Any 1) 4 marks**

1. ABCD is a parallelogram. Point E is on side BC, line DE intersects Ray AB in point T. Prove that : DE × BE = CE × TE.

2. In trapezium PQRS, side PQ || side SR. AR = 5AP and AS = 5AQ. Prove that : SR = 5PQ.