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 axiom

Solution:

The figure represents a triangle ABC.

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

Given, BX = AB/2 ------------ (1)

BY = BC/2 --------------------- (2)

Also, AB = BC ---------------- (3)

We have to show that BX = BY

From (1), AB = 2BX

This implies X is the midpoint of AB

From (2), BC = 2BY

This implies Y is the midpoint of BC

Using Euclid’s axiom,

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

From (3), 2BX = 2BY

Therefore, BX = BY

✦ Try This: If one angle of a triangle is equal to the sum of the other two angles, then the triangle is (a) an isosceles triangle, (b) an obtuse triangle, (c) an equilateral triangle, (d) a right triangle

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

NCERT Exemplar Class 9 Maths Exercise 5.3 Problem 6

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 axiom

Summary:

In Fig.5.6, we have BX = 1/2 AB, BY = 1/2 BC and AB = BC. We observe that X and Y are the midpoints of AB and BC. By Euclid’s axiom, it is shown that BX = BY

☛ Related Questions:

• 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
• In the Fig. 5.9, we have ∠ABC = ∠ACB, ∠3 = ∠4. Show that ∠1 = ∠2. Solve using Euclid’s axiom