Question

Prove that triangle VWX is isosceles by demonstrating that two of its sides are of equal length.in

Answer 1

To prove that triangle VWX is isosceles, assume VX = VZ and use the Pythagorean theorem to determine the lengths of the other sides. If we substitute a = b in equation (1), we get: a^2 + c^2 = a^2. This means that c, which represents the length of side WX, must be zero. However, a triangle cannot have a side with zero length, so our assumption that VX = VZ must be incorrect. Thus, triangle VWX is not isosceles.

Step-by-step explanation:

To prove that triangle VWX is isosceles, we need to demonstrate that two of its sides are of equal length. Let's assume that VX = VZ. From there, we can use the Pythagorean theorem to determine the lengths of the other sides. Let's say VX = a, VZ = b, and WX = c. According to the Pythagorean theorem, we have the following equations:

a^2 + c^2 = b^2 (1)

b^2 + c^2 = a^2 (2)

If we substitute a = b in equation (1), we get:

a^2 + c^2 = a^2

c^2 = 0

This means that c, which represents the length of side WX, must be zero. However, a triangle cannot have a side with zero length, so our assumption that VX = VZ must be incorrect. Thus, we can conclude that triangle VWX is not isosceles.