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All questions of Quadrilaterals for Class 9 Exam
In a parallelogram the sum of two consecutive angles is- a)360°
- b)100°
- c)180°
- d)90°
Correct answer is option 'C'. Can you explain this answer?
In a parallelogram the sum of two consecutive angles is
a)
360°
b)
100°
c)
180°
d)
90°
|
|
Maroof Khan answered |
Because sum of parallelogram is 180degree
Which of the following is not true for a parallelogram? - a)Diagonals bisect each other
- b)Opposite sides are equal
- c)Opposite angles are equal
- d)Opposite angles are bisected by the diagonals
Correct answer is option 'D'. Can you explain this answer?
Which of the following is not true for a parallelogram?
a)
Diagonals bisect each other
b)
Opposite sides are equal
c)
Opposite angles are equal
d)
Opposite angles are bisected by the diagonals
|
Imk Pathshala answered |
The statement that opposite angles are bisected by the diagonals is not generally true. This property does not hold for every parallelogram; it only occurs in special cases such as a rectangle or a rhombus under certain conditions.
Thus, the option that is not always true for a parallelogram is:
Option D: Opposite angles are bisected by the diagonals.
Option D: Opposite angles are bisected by the diagonals.
ABCD is a parallelogram in which the bisectors of angles ∠A and ∠B intersect at point P then ∠APB is
- a)45°
- b)90°
- c)60°
- d)80°
Correct answer is option 'B'. Can you explain this answer?
ABCD is a parallelogram in which the bisectors of angles ∠A and ∠B intersect at point P then ∠APB is
a)
45°
b)
90°
c)
60°
d)
80°
|
|
Imk Pathshala answered |
Since ABCD is a Parallelogram. Therefore,
AD || BC
AB is a transversal . Therefore ,
A + B = 180°. [ Consecutive interior angles]
Multiply both sides by 1/2 ,
1/2 A + 1/2 B = 1/2 (180°)
1/2 A + 1/2 B = 90° __【1】
Since, AP and PB are angle bisectors of A and B . Therefore,
Angle 1 = 1/2 A
Angle 2 = 1/2 B
Substitute the values in【1】,
Angle 1 + Angle 2 = 90°____【2】
Now, in ∆ APB,
1 + APB + 2 = 180°
90° + APB = 180°. [From 【2】]
APB = 90°
- HENCE PROVED
AD || BC
AB is a transversal . Therefore ,
A + B = 180°. [ Consecutive interior angles]
Multiply both sides by 1/2 ,
1/2 A + 1/2 B = 1/2 (180°)
1/2 A + 1/2 B = 90° __【1】
Since, AP and PB are angle bisectors of A and B . Therefore,
Angle 1 = 1/2 A
Angle 2 = 1/2 B
Substitute the values in【1】,
Angle 1 + Angle 2 = 90°____【2】
Now, in ∆ APB,
1 + APB + 2 = 180°
90° + APB = 180°. [From 【2】]
APB = 90°
- HENCE PROVED
Chapter doubts & questions for Quadrilaterals - Mathematics (Maths) Class 9 2025 is part of Class 9 exam preparation. The chapters have been prepared according to the Class 9 exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Class 9 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
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