In the Fig. 5.1, if ∠1 = ∠3, ∠2 = ∠4 and ∠3 = ∠4, write the relation between ∠1 and ∠2, using an Euclid’s axiom

Solution:

Given, ∠1 = ∠3, ∠2 = ∠4 and ∠3 = ∠4

We have to write the relation between ∠1 and ∠2 using an Euclid’s axiom.

Euclid’s first axiom states that the things which are equal to the same thing are equal to one another.

∠1 = ∠3

Also, ∠3 = ∠4

Now, ∠1 = ∠3 = ∠4

Given, ∠2 = ∠4

So, ∠1 = ∠2 = ∠3 = ∠4

Therefore, all the angles are equal to one another.

✦ Try This: If ∠1 = 120°, find the measures of : ∠2, ∠3, ∠4, ∠5, ∠6, ∠7 and ∠8. Give reasons.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 5

NCERT Exemplar Class 9 Maths Exercise 5.3 Sample Problem 3

In the Fig. 5.1, if ∠1 = ∠3, ∠2 = ∠4 and ∠3 = ∠4, write the relation between ∠1 and ∠2, using an Euclid’s axiom

Summary:

In the Fig. 5.1, if ∠1 = ∠3, ∠2 = ∠4 and ∠3 = ∠4, the relation between ∠1 and ∠2, using Euclid’s first axiom we observe that all the angles are equal to one another

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