Discussion
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- Question
- In the given figure, which of the following is true :
Options- A. x = ? + ? + ?
- B. x + ? = ? + ?
- C. x + ? = ? + ?
- D. x + ? = ? + ?
- Correct Answer
- x = ? + ? + ?
ExplanationFrom 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 = ? + ? + ? - 1. 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
- 2. 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
- 3. 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
- 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
- 5. 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
- 6. 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
- 7. 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
- 8. If the sides of a right triangle are x, x + 1 and x ? 1, then the hypotenuse :
Options- A. 5
- B. 4
- C. 1
- D. 0 Discuss
- 9. ABCD is a square, F is mid point of AB and E is a point on BC such that BE is one-third of BC. If area of ?FBE = 108 m 2, then the length of AC is:
Options- A. 63 m
- B. 36?2 m
- C. 63?2 m
- D. 72?2 m Discuss
- 10. ABCD is a parallelogram P, Q, R and S are points on sides AB, BC, CD and DA respectively such that AP = DR. If the area of the parallelogram ABCD is 16 cm 2, then the area of the quadrilateral PQRS is:
Options- A. 6 cm2
- B. 6.4 cm2
- C. 4 cm2
- D. 8 cm2 Discuss
Plane Geometry problems
Search Results
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 .
Correct Answer: 25 81
Explanation:
Correct Answer: CD = ab b+c
Explanation:
Correct Answer: 9 16
Explanation:
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 }
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.
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.
Correct Answer: 5
Explanation:
From given figure , we have
Let, (x + 1) be the hypotenuse and perpendicular = x - 1 , base = x.
By pythagoras theorem ,
? (x + 1)2 = x2 + (x + 1)2 ? x = 4
? Hypotenuse = 4 + 1 = 5
Correct Answer: 36?2 m
Explanation:
Correct Answer: 8 cm2
Explanation:
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