Plane Geometry problems
- 1. The sides AB and AC of ?ABC have been produced to D and E respectively. The bisectors of ?CBD and ?BCE meet at O. If ?A = 40°, then ?BOC is equal to:
Options- A. 60°
- B. 65°
- C. 75°
- D. 70° Discuss
Correct Answer: 70°
Explanation:
- 2. In the given figure, DE || BC if AD = 1.7 cm, AB = 6.8 cm and AC = 9 cm, find AE.
Options- A. 2.25cm
- B. 4.5cm
- C. 1.25cm
- D. 2.5cm Discuss
Correct Answer: 2.25cm
Explanation:
- 3. If the bisector of an angle of ? bisects the opposite side, then the ? is :
Options- A. Scalene
- B. Isosceles
- C. Right triangle
- D. circle Discuss
Correct Answer: Isosceles
Explanation:
- 4. The areas of two similar ?s are 81 cm 2 and 144 cm 2. If the largest side of the smaller ? is 27 cm, then the largest side of the larger ? is :
Options- A. 24 cm
- B. 48 cm
- C. 36 cm
- D. 88 cm Discuss
Correct Answer: 36 cm
Explanation:
- 5. In the given figure ?BAD = ?CAD. AB = 4 cm, AC = 5.2 cm, BD = 3 cm. Find BC.
Options- A. 6.9 cm
- B. 9.6 cm
- C. 3.9 cm
- D. 9.3 cm Discuss
Correct Answer: 6.9 cm
Explanation:
- 6. A ladder 15 m long reaches a window which is 9 m above the ground on one side of street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 12 m high. What is the width of the street:
Options- A. 31 m
- B. 12 m
- C. 30 m
- D. 21 m Discuss
Correct Answer: 21 m
Explanation:
Draw a figure as per given question,
In a Right triangle ADC, Use the (Pythagoras Theorem)
AC = ?DC2 - AD2
? AC = ? 152 - 9 2
? AC = ? 225 - 81
? AC = ? 144
? AC = 12 cm
In a Right triangle BCE, Use the formula
CB = ? CD2 - BE2
? CB = ?15 2 - 122
? CB = ?225 - 144
? CB = ? 81
? CB = 9 m
? Width of the street (AC + BC) = AB = 12 + 9 = 21 m.
- 7. D and E are the points on the sides AB and AC respectively of ?ABC such that AD = 8 cm, BD = 12 cm, AE = 6 cm and EC = 9 cm. Then find BC/ DE.
Options- A. 5 2
- B. 2 5
- C. 5 7
- D. 5 3 Discuss
Correct Answer: 5 2
Explanation:
- 8. In an equilateral ? ABC, if AD ? BC, then which option is true?
Options- A. 3AB2 = 2AD2
- B. 2AB2 = 3AD2
- C. 3AB2 = 4AD2
- D. 4AB2 = 3AD2 Discuss
Correct Answer: 3AB2 = 4AD2
Explanation:
- 9. In the given figure, AB || DC, find the value of x.
Options- A. x = 8
- B. x = 9
- C. x = 8 or 9
- D. x = 10 Discuss
Correct Answer: x = 8 or 9
Explanation:
- 10. In the adjoining figure ?A + ?B + ?C + ?D + ?E + ?F =?
Options- A. 270°
- B. 300°
- C. 360°
- D. 330° Discuss
Correct Answer: 360°
Explanation:
In ?ACE
?A + ?C + ?E = 180°
Similarly in ?DFB
?D + ?F + ?B = 180°
? (?A + ?C + ?E) + (?D + ?F + ?B) = 360°
?A + ?B + ?C + ?D + ?E + ?F = 360°
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