In a parallelogram, if each angle is equal, then it is called.
A) Rectangle
B) Square
C) Rhombus
D) None of these
Answer
658.8k+ views
Hint: First find the measure of each angle of the parallelogram using the condition that the measure of each angle is equal and then use the property of parallelogram to find the required result.
In any parallelogram, if all the angles are equal then they must be of $90^\circ $ or we can say that all angles must be right angles because the sum of all the angles of a parallelogram is 360 degree.
Complete step-by-step answer:
We have given a parallelogram having each angle equal to each other and we have to find whether it is rectangle, square, rhombus, or none of them.
Firstly, we know that the sum of all angles of a quadrilateral is $360^\circ $.
Now, assume that each angle of the rectangle is $x$, then using the property of sum of angles of quadrilateral:
$x + x + x + x = 360^\circ $
$4x = 360^\circ $
$x = 90^\circ $
So, the measure of each angle of the quadrilateral is $90^\circ $.
Now, in a parallelogram, the opposite sides are equal and parallel to each other and we have each angle of $90^\circ $.
Take a look at the figure that has all these properties:
So, a rectangle satisfies all these given conditions because in a rectangle each angle is a right angle and opposite sides are equal and parallel to each other.
So, rectangles satisfy these given conditions in all forms.
Therefore, the correct option for the answer is option A which is a rectangle.
Note: In this problem, we cannot take square because it may satisfy the condition given that right and parallel and equal opposite sides but for square, we need one more condition which is all the sides must be equal to each other.
In any parallelogram, if all the angles are equal then they must be of $90^\circ $ or we can say that all angles must be right angles because the sum of all the angles of a parallelogram is 360 degree.
Complete step-by-step answer:
We have given a parallelogram having each angle equal to each other and we have to find whether it is rectangle, square, rhombus, or none of them.
Firstly, we know that the sum of all angles of a quadrilateral is $360^\circ $.
Now, assume that each angle of the rectangle is $x$, then using the property of sum of angles of quadrilateral:
$x + x + x + x = 360^\circ $
$4x = 360^\circ $
$x = 90^\circ $
So, the measure of each angle of the quadrilateral is $90^\circ $.
Now, in a parallelogram, the opposite sides are equal and parallel to each other and we have each angle of $90^\circ $.
Take a look at the figure that has all these properties:
So, a rectangle satisfies all these given conditions because in a rectangle each angle is a right angle and opposite sides are equal and parallel to each other.
So, rectangles satisfy these given conditions in all forms.
Therefore, the correct option for the answer is option A which is a rectangle.
Note: In this problem, we cannot take square because it may satisfy the condition given that right and parallel and equal opposite sides but for square, we need one more condition which is all the sides must be equal to each other.
Recently Updated Pages
Explain the Treaty of Vienna of 1815 class 10 social science CBSE

10 examples of friction in our daily life

Draw a diagram of nephron and explain its structur class 11 biology CBSE

Write structures of the following compounds i 2 Chloro3methylpentane class 11 chemistry CBSE

A Paragraph on Pollution in about 100-150 Words

XIX+XXX A 49 B 51 C 55 D 44 class 5 maths CBSE

Trending doubts
What is BLO What is the full form of BLO class 8 social science CBSE

Citizens of India can vote at the age of A 18 years class 8 social science CBSE

Full form of STD, ISD and PCO

Write an article on Global warming in about 200 words

What are the methods of reducing friction. Explain

What is the collective noun for soldiers class 8 english CBSE

