In the Fig. 5.8, we have ∠1 = ∠3 and ∠2 = ∠4. Show that ∠A = ∠C. Solve using Euclid’s axiom

Solution:

The figure represents a quadrilateral ABCD.

Given, ∠1 = ∠3 -------------- (1)

Also, ∠2 = ∠4 ---------------- (2)

We have to show that ∠A = ∠C.

On adding (1) and (2),

∠1 + ∠2 = ∠3 + ∠4

By using Euclid’s axiom,

If equals are added to the equals, the wholes are equal.

From the figure,

∠1 + ∠2 = ∠A

∠3 + ∠4 = ∠C

Therefore, ∠A = ∠C

✦ Try This: A transversal intersects two lines in such a way that the two interior angle on the same side of transversal are equal.Will the two lines always be parallel?

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

NCERT Exemplar Class 9 Maths Exercise 5.3 Problem 8

In the Fig. 5.8, we have ∠1 = ∠3 and ∠2 = ∠4. Show that ∠A = ∠C. Solve using Euclid’s axiom

Summary:

The figure represents a quadrilateral ABCD. In the Fig. 5.8, we have ∠1 = ∠3 and ∠2 = ∠4. By using Euclid’s axiom, it is shown that ∠A = ∠C

☛ Related Questions:

• 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
• In the Fig. 5.11, if OX = 1/2 XY, PX = 1/2 XZ and OX = PX, show that XY = XZ..Solve using Euclid’s a . . . .