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Test: Angle Relations In Parallelogram - Class 9 MCQ


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10 Questions MCQ Test - Test: Angle Relations In Parallelogram

Test: Angle Relations In Parallelogram for Class 9 2024 is part of Class 9 preparation. The Test: Angle Relations In Parallelogram questions and answers have been prepared according to the Class 9 exam syllabus.The Test: Angle Relations In Parallelogram MCQs are made for Class 9 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Angle Relations In Parallelogram below.
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Test: Angle Relations In Parallelogram - Question 1

In a parallelogram the sum of two consecutive angles is

Detailed Solution for Test: Angle Relations In Parallelogram - Question 1

The sum of any two consecutive angles in a parallelogram is always 180°.

Test: Angle Relations In Parallelogram - Question 2

Bisectors of angles of a parallelogram form a

Detailed Solution for Test: Angle Relations In Parallelogram - Question 2

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Test: Angle Relations In Parallelogram - Question 3

In a parallelogram PQRS, if diagonal PR bisects the ∠P, then it also bisects _____.

Test: Angle Relations In Parallelogram - Question 4

Which of the following statements is true about the diagonal of a parallelogram?

Detailed Solution for Test: Angle Relations In Parallelogram - Question 4

Answer: A
Solution:
A diagonal of a parallelogram divides the parallelogram into two congruent triangles. This is a fundamental property of parallelograms as stated in Theorem 8.1.
Correct Answer: (A) A diagonal of a parallelogram divides it into two congruent triangles.

Test: Angle Relations In Parallelogram - Question 5

ABCD is a parallelogram in which the bisectors of angles ∠A and ∠B intersect at point P then ∠APB is

Detailed Solution for Test: Angle Relations In Parallelogram - Question 5

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

Test: Angle Relations In Parallelogram - Question 6

Which of the following statements correctly proves that each angle of a rectangle is a right angle?

Detailed Solution for Test: Angle Relations In Parallelogram - Question 6

Answer: C
Solution:
A rectangle is a parallelogram where one angle is a right angle (90 degrees). Using the properties of parallelograms:

  1. Interior angles on the same side of the transversal add up to 180 degrees
  2. Opposite angles are equal.

Since one angle is 90 degrees , all other angles (∠B,∠C,∠D)  are also 90 degrees
Correct Answer: (C) A rectangle is a parallelogram where one angle is a right angle, and all opposite and adjacent angles are equal to 90°.

Test: Angle Relations In Parallelogram - Question 7

In a triangle, the line segment joining the midpoints of two sides has which of the following properties?

Detailed Solution for Test: Angle Relations In Parallelogram - Question 7

Answer: C
Solution:
In a triangle, if a line segment joins the midpoints of two sides, it is parallel to the third side and half of its length. This is derived from the property of midpoints and parallelograms formed in the figure.
Correct Answer: (C) It is parallel to the third side and half of its length.

Test: Angle Relations In Parallelogram - Question 8

 Which of the following is not true for a parallelogram?    

Detailed Solution for Test: Angle Relations In Parallelogram - Question 8

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.

Test: Angle Relations In Parallelogram - Question 9

If PQRS is a parallelogram, then ∠Q – ∠S is equal to:

Detailed Solution for Test: Angle Relations In Parallelogram - Question 9

In a parallelogram, opposite angles are always equal. Since ∠Q and ∠S are opposite angles, it follows that:

∠Q = ∠S

Therefore:

∠Q – ∠S = 0°

The correct answer is D: 0°.

Test: Angle Relations In Parallelogram - Question 10

AN and CP are perpendiculars to the diagonal BD of a parallelogram ABCD. Choose the correct option

Detailed Solution for Test: Angle Relations In Parallelogram - Question 10

Here, AN and CP are perpendiculars dropped from points A and C, respectively, to the diagonal BD of the parallelogram ABCD.

From properties of parallelograms and the perpendiculars drawn from vertices to the diagonal, it can be concluded that the two perpendiculars AN and CP must be equal in length. This is because in any parallelogram, the perpendicular distances from opposite vertices to the diagonal are always equal.

Thus, the correct option is: d) AN = CP

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