In the Fig.5.7, we have ∠1 = ∠2, ∠2 = ∠3. Show that ∠1 = ∠3. Solve using Euclid’s axiom

Solution:

The figure represents a quadrilateral ABCD.

Given, ∠1 = ∠2 ------------------ (1)

Also, ∠2 = ∠3 -------------------- (2)

We have to show that ∠1 = ∠3.

From (1) and (2),

∠1 = ∠2 = ∠3

By using Euclid’s axiom,

The things which are equal to the same thing are equal to one another.

Therefore, ∠1 = ∠3

✦ Try This: An exterior angle of a triangle is 110° and its two interior opposite angles are equal. Find each of these equal angles.

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

NCERT Exemplar Class 9 Maths Exercise 5.3 Problem 7

In the Fig.5.7, we have ∠1 = ∠2, ∠2 = ∠3. Show that ∠1 = ∠3. Solve using Euclid’s axiom

Summary:

Fig.5.7 is a quadrilateral ABCD, we have ∠1 = ∠2, ∠2 = ∠3. By using Euclid’s axiom, it is shown that ∠1 = ∠3

☛ Related Questions:

• In the Fig. 5.8, we have ∠1 = ∠3 and ∠2 = ∠4. Show that ∠A = ∠C. Solve using Euclid’s axiom
• In the Fig. 5.9, we have ∠ABC = ∠ACB, ∠3 = ∠4. Show that ∠1 = ∠2. Solve using Euclid’s axiom
• In the Fig. 5.10, we have AC = DC, CB = CE. Show that AB = DE. Solve using Euclid’s axiom