Q.1. Two isosceles triangles have equal angles and their areas are in the ratio 16: 25. The ratio of corresponding heights is:
AnswerAnswer: (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 cm2, find the area of ΔPOB.
(A) 233 cm2
(B) 294 cm2
(C) 300 cm2
(D) 420 cm2
AnswerAnswer: (B) 294 cm2
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?
AnswerAnswer: (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.
AnswerAnswer: (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
AnswerAnswer: (C) 3:4
Q.6. ABCD is a parallelogram with diagonal AC If a line XY is drawn such that XY ∥ AB. BX/XC=?
AnswerAnswer: (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) = (AD2/AB2)
(iii) (area of △ ADE/ area of △ ABC)= (AB2/ AD2)
(A) only (iii)
(B) only (i)
(C) only (i) and (ii)
(D) all (i) , (ii) and (iii)
AnswerAnswer: (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
AnswerAnswer: (B) 1:1
Q.9. In ΔABC, AC = 15 cm and DE || BC. If AB/AD=3, Find EC.
(B) 10 cm
AnswerAnswer: (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
AnswerAnswer: (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°
AnswerAnswer: (B) 75°
Q.12. The triangles ABC and ADE are similar
Which of the following is true?
(D) All of the Above
AnswerAnswer: (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
AnswerAnswer: (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
AnswerAnswer: (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.
AnswerAnswer: (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) a2 = b2 + c2 – bc
(B) a2 = b2 + c2 + bc
(C) a2 = b2 + c2 – 2bc
(D) a2 = b2 + c2 + 2bc
AnswerAnswer: (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 :
AnswerAnswer: (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?
AnswerAnswer: (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
AnswerAnswer: (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