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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.

Is the following statement true? Why? “Two quadrilaterals are similar if their corresponding angles are equal”

Solution:

Given, the corresponding angles of two quadrilaterals are equal.

We have to determine if the two quadrilaterals are similar.

By the property of similarity,

To prove two figures are similar we must prove that their corresponding angles are congruent and their corresponding sides are in proportion.

Here, the corresponding angles are equal but no details about the sides are mentioned.

Is the following statement true? Why? “Two quadrilaterals are similar, if their corresponding angles are equal”

For example: Consider a rectangle and a square

The corresponding angles are equal to 90 degrees.

The ratio of corresponding sides are

DA/PS = 5/2

DC/SR = 5/4

BC/RQ = 5/2

AB/PQ = 5/4

It is clear that the corresponding angles are equal but the corresponding sides are not in proportion.

So, the given quadrilaterals are not similar.

Therefore, the two quadrilaterals cannot be similar only if their corresponding angles are equal.

✦ Try This: Is the following statement true? Why? “Two quadrilaterals are similar if their corresponding sides are in proportion”

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6

NCERT Exemplar Class 10 Maths Exercise 6.2 Problem 6

Is the following statement true? Why? “Two quadrilaterals are similar if their corresponding angles are equal”

Summary:

The statement “Two quadrilaterals are similar if their corresponding angles are equal” is false

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