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 using Euclid’s axiom

Solution:

The figure represents a triangle ABC.

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

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

Also, AX = CY ------------------------ (2)

We have to show that AC = BC.

Since X is the midpoint of AC

AC = 2AX = 2CX -------------------- (3)

Since Y is the midpoint of BC

BC = 2BY = 2CY --------------------- (4)

According to Euclid’s axiom,

Things which are double of the same thing are equal to one another.

Using (2) in (3),

2AX = 2CY ------------------- (5)

Using (5) in (3) and (4),

AC = 2AX = 2CY

BC = 2CY = 2AX

Therefore, AC = BC

✦ Try This: If two lines intersect prove that the vertically opposite angles are equal.

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

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NCERT Exemplar Class 9 Maths Exercise 5.3 Problem 5

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 using Euclid’s axiom

Summary:

In Fig.5.5, we have X and Y are the mid-points of AC and BC and AX = CY. Using Euclid’s axiom, it is shown that AC = BC

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☛ Related Questions:

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