Plane Geometry problems
- 1. A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At the same time a tower casts the shadow 40 m long on the ground. Find the height of the tower.
Options- A. 600 m
- B. 160 m
- C. 60 m
- D. 52 m Discuss
Correct Answer: 60 m
Explanation:
- 2. In a right angled ? ABC, Right angled at A, AD ? BC. Then :
Options- A. AD2 = BD × CD
- B. AD2 = AB × AC
- C. AD2 = BD × AB
- D. AD2 = CD × AC Discuss
Correct Answer: AD2 = BD × CD
Explanation:
- 3. If ABCD is a parallelogram and AC and BD be its diagonals, then:
Options- A. AB2 + BC2+ CD2+ DA2 = AC2 ? BD2
- B. AB2 + BC2+ CD2 + DA2 = AC2 + BD2
- C. 4AD2 = 2AC2 + 2BD2
- D. 4AB2 = 2AC2 ? 2BC2 Discuss
Correct Answer: AB2 + BC2+ CD2 + DA2 = AC2 + BD2
Explanation:
In ||gm ABCD , we have
Since diagonals of parallelogram(||gm ) bisect each other,
? M will be the mid-point of each of the diagonal AC and BD
? In ?ABC AB2 + BC2 = 2(AM2 + MB2) ......... ( 1 ) [Appolonius Theorem]
In ?ADC AD2 + CD2 = 2(AM2 + DM2) ......... ( 2 )
= 2(AM2 + MB2) [? DM = BM]
Adding equations ( 1 ) and ( 2 )
AB2 + BC2 + CD2 + DA2 = 2(AM2 + MB2 + 2(AM2 + MB2 = 4AM2 + 4MB2
= (2AM)2 + (2MB)2= AC2+ BD2. { ? AM = MC , MB = MD }
- 4. In the given figure, DE || BC and DE : BC = 3 : 5 the ratio of the areas of ? ADE and the trapezium BCED.
Options- A. 9 25
- B. 12 25
- C. 3 4
- D. 9 16 Discuss
Correct Answer: 9 16
Explanation:
- 5. In a ? ABC, AD intersects ? A and BC. If BC = a, AC = b and AB = c, Then :
Options- A. CD = b+c ab
- B. CD = ab b+c
- C. CD = bc+ab ac
- D. CD = ac cb+ab Discuss
Correct Answer: CD = ab b+c
Explanation:
- 6. In the given figure DE||BC and AD : DB = 5 : 4,
Then ar(?DFE) ar(?CFB)
Options- A. 25 81
- B. 25 16
- C. 16 25
- D. 16 81 Discuss
Correct Answer: 25 81
Explanation:
- 7. In center of a triangle lies in the interior of :
Options- A. an isosceles triangle only
- B. any triangle
- C. an equilateral triangle only
- D. a right triangle only Discuss
Correct Answer: any triangle
Explanation:
We know that In center of every triangle ( acute , obtuse and right angle ) lies in its interior.
Hence required answer will be any triangle .
- 8. In the given figure, which of the following is true :
Options- A. x = ? + ? + ?
- B. x + ? = ? + ?
- C. x + ? = ? + ?
- D. x + ? = ? + ? Discuss
Correct Answer: x = ? + ? + ?
Explanation:
From above figure , we can see that
Join B and D and produce BD to E
Then, p + q = ? and s + t = x
We know that , Exterior angle = Sum of two interior angle
Now, s = p + ? (Exterior angle of a ? prop.)
Similarly, t = q + ? (Exterior angle of a ? prop.)
Adding, s + t = p + q + ? + ?
Putting s + t = x and p + q = ? ,
Hence x = ? + ? + ?
- 9. In the given figure, the side BC of a ? ABC is produced on both sides. Then ? 1 + ? 2 is equal to :
Options- A. ?A + 180°
- B. 180° ? ?A
- C. 1 (?A + 180°) 2
- D. ?A + 90° Discuss
Correct Answer: ?A + 180°
Explanation:
From the given figure, In ?ABC
We know that , Exterior angle = Sum of two interior angles
?1 = ?A + ?5 ................. ( 1 )
and ?2 = ?A + ?6 ................. ( 2 )
Adding equations ( 1 ) and ( 2 ).
?1 + ?2 = 2?A + ?5 + ?6
= 2?A + (180° ? ?A) = ?A + 180°
The given question can be restated as the sum of two exterior angles exceeds ?A of the ?ABC by 2 right angles.
- 10. If two diameters of a circle intersect each other at right angles, then the quadrilateral formed by joining here end points is a :
Options- A. Rhombus
- B. Rectangle
- C. Square
- D. Parallelogram Discuss
Correct Answer: Square
Explanation:
From given figure , we have
In quadrilateral ABCD , we can see that
Diagonal AB = Diagonal CD ......... ( ? )
AO = OB ......... ( ? )
DO = CO ......... ( ? )
?DOB = 90° ......... ( ? )
From ( ? ) , ( ? ) , ( ? ) and ( ? ) , we get
From above , it is clear that In quadrilateral ABCD , diagonals are equal and they bisect each other at 90° .
? Quadrilateral ABCD is square.
More in Aptitude:
Programming
Copyright ©CuriousTab. All rights reserved.