# In Fig.5.4, we have AB = BC, BX = BY. Show that AX = CY. Solve using Euclid’s axiom

**Solution:**

The figure represents a triangle ABC.

The points X and Y lie on the sides AB and BC of the triangle ABC.

Given, AB = BC --------- (1)

Also, BX = BY ----------- (2)

We have to show that AX = CY

From the figure,

AB = AX + BX

So, AB - BX = AX ------------- (3)

Similarly,

BC = BY + CY

BC - BY = CY ------------------- (4)

By using Euclid’s axiom,

If equals be subtracted from equals, the remainders are equal.

Using (1) and (2) in (3) and (4),

AB - BX = BC - BY

Therefore, AX = CY

**✦ Try This:** Prove that two lines that are respectively perpendicular to two intersecting lines intersect each other.

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

**NCERT Exemplar Class 9 Maths Exercise 5.3 Problem 4**

## In Fig.5.4, we have AB = BC, BX = BY. Show that AX = CY. Solve using Euclid’s axiom

**Summary:**

The given figure is a triangle ABC with points X and Y lying on the sides AB and BC. We have AB = BC, BX = BY. By using Euclid’s axiom it is shown that AX = CY

**☛ Related Questions:**

- In Fig.5.5, we have X and Y are the mid-points of AC and BC and AX = CY. Show that AC = BC. Solve us . . . .
- In Fig.5.6, we have BX = 1/2 AB, BY = 1/2 BC and AB = BC. Show that BX = BY. Solve using Euclid’s ax . . . .
- In the Fig.5.7, we have ∠1 = ∠2, ∠2 = ∠3. Show that ∠1 = ∠3. Solve using Euclid’s axiom

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