**Q.1. Two isosceles triangles have equal angles and their areas are in the ratio 16: 25. The ratio of corresponding heights is:**

(A) 4:5

(B) 5:4

(C) 3:2

(D) 5:7

**Answer**

Answer: (A) 4:5
**Q.2. In the figure, PB and QA are perpendicular to segment AB. If OA = 5 cm, PO = 7cm and area (ΔQOA) = 150 cm ^{2}, find the area of ΔPOB.**

(A) 233 cm^{2}

(B) 294 cm^{2}

(C) 300 cm^{2}

(D) 420 cm^{2}

**Answer**

Answer: (B) 294 cm^{2}

**Q.3. In a right △ABC, a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does not give the ratio of the areas of △ABD and △ACB?**

(A) (AB/AC)^{2}

(B) (AD/AB)^{2}

(C) (AB/AD)^{2}

(D) (BD/CB)^{2}

**Answer**

Answer: (C) (AB/AD)^{2}

**Q.4. If △ ABC ~ △ DEF such that AB = 12 cm and DE = 14 cm. Find the ratio of areas of △ ABC and △ DEF.**

(A) 49/9

(B) 36/49

(C) 49/16

(D) 25/49

**Answer**

Answer: (B) 36/49
**Q.5. In △ABC, AB = 3 and, AC = 4 cm and AD is the bisector of ∠A. Then, BD : DC is —**

(A) 9: 16

(B) 4:3

(C) 3:4

(D) 16:9

**Answer**

Answer: (C) 3:4
**Q.6. ABCD is a parallelogram with diagonal AC If a line XY is drawn such that XY ∥ AB. BX/XC=?**

(A) (AY/AC)

(B) DZ/AZ

(C) AZ/ZD

(D) AC/AY

**Answer**

Answer: (C) AZ/ZD
**Q.7. D and E are points on the sides AB and AC respectively of a △ABC such that DE || BC. Which of the following statement is true?**

(i) △ ADE ~ △ ABC

(ii) (area of △ ADE/ area of △ ABC) = (AD^{2}/AB^{2})

(iii) (area of △ ADE/ area of △ ABC)= (AB^{2}/ AD^{2})

(A) only (iii)

(B) only (i)

(C) only (i) and (ii)

(D) all (i) , (ii) and (iii)

**Answer**

Answer: (C) only (i) and (ii)
**Q.8. In ABC, Given that DE//BC, D is the midpoint of AB and E is a midpoint of AC. The ratio AE: EC is __.**

(A) 1: 3

(B) 1:1

(C) 2:1

(D) 1:2

**Answer**

Answer: (B) 1:1
**Q.9. In ΔABC, AC = 15 cm and DE || BC. If AB/AD=3, Find EC.**

(A) 5cm

(B) 10 cm

(C) 2.5cm

(D) 9cm

**Answer**

Answer: (B) 10 cm
**Q.10. △ ABC is an acute angled triangle. DE is drawn parallel to BC as shown. Which of the following are always true?**

i) △ ABC ∼ △ ADE

ii) AD/BD= AE/EC

iii) DE= BC/2

(A) Only (i)

(B) (i) and (ii) only

(C) (i), (ii) and (iii)

(D) (ii) and (iii) only

**Answer**

Answer: (B) (i) and (ii) only
**Q.11. In △ ABC and △ DEF, ∠A = ∠E = 40∘ and AB/ED=AC/EF. Find ∠B if ∠F is 65°**

(A) 85°

(B) 75°

(C) 35°

(D) 65°

**Answer**

Answer: (B) 75°
**Q.12. The triangles ABC and ADE are similar**

**Which of the following is true?**

(A) EC/AC=AD/DE

(B) BC/BD=CE/DE

(C) AB/AD=BC/DE

(D) All of the Above

**Answer**

Answer: (C) AB/AD=BC/DE
**Q.13. The ratio of the corresponding sides of two similar triangles is 1: 3. The ratio of their corresponding heights is**

(A) 1:3

(B) 3:1

(C) 1:9

(D) 9:1

**Answer**

Answer: (A) 1:3
**Q.14. If in △ CAB and △ FED, AB/ EF=BC/FD=AC/ED, then:**

(A) △ ABC∼△ DEF

(B) △ CAB∼△ DEF

(C) △ ABC∼△ EFD

(D) △ CAB∼△ EFD

**Answer**

Answer: (C) △ ABC∼△ EFD
**Q.15. A tower of height 24m casts a shadow 50m and at the same time, a girl of height 1.8m casts a shadow. Find the length of the shadow of girl.**

(A) 3.75m

(B) 3.5m

(C) 3.25m

(D) 3m

**Answer**

Answer: (A) 3.75 m
**Q.16. In the adjoining figure, if BC = a, AC = b, AB = c and ∠CAB = 120°, then the correct relation is-**

(A) a^{2} = b^{2} + c^{2} – bc

(B) a^{2} = b^{2} + c^{2} + bc

(C) a^{2} = b^{2} + c^{2} – 2bc

(D) a^{2} = b^{2} + c^{2} + 2bc

**Answer**

Answer: (B) a2 = b2 + c2 + bc
**Q.17. If the distance between the top of two trees 20 m and 28 m tall is 17 m, then the horizontal distance between the trees is :**

(A) 11m

(B) 31m

(C) 15m

(D) 9m

**Answer**

Answer: (C) 15m
**Q.18. In the figure △ABC is a right angled triangle with right angle at B. BD is perpendicular to AC. Then which of the following options will hold true?**

(A) AD^{2}=DC×AC

(B) AB^{2}=AD×AC

(C) AB^{2}=AD×DC

(D) AB^{2}=DC^{2}+AD^{2}

**Answer**

Answer: (B) AB2=AD×AC
**Q.19. If Δ ABC and Δ DEF are similar such that 2AB = DE and BC = 8 cm, then Find EF.**

(A) 16 cm

(B) 12 cm

(C) 8 cm

(D) 4 cm

**Answer**

Answer: (A) 16 cm
**Q.20. △ ABC is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm.△ DEF is similar to △ABC. If EF = 4 cm, then the perimeter of △DEF is –**

(A) 7.5 cm

(B) 15cm

(C) 30cm

(D) 22.5cm