If the perpendicular bisector of one side of a triangle goes through the opposite vertex, then is the triangle ( sometimes, always, or never) isosceles

It is always isosceles because it can be proved as follows:

The perpendicular bisector dissects the triangle into two, and it is the common side. Then each side of the bisector is 90 degrees, and the bisected to two equal sides, so the two dissected triangles are congruent, hence the original triangle is isosceles.

Answer Link

YashBhattar YashBhattar · Answer 2 · 2022-05-31T13:08:51+02:00

If the perpendicular bisector of one side of a triangle goes through the opposite vertex, then is the triangle is always isosceles

What is Isosceles triangle?

An isosceles triangle is a triangle that has two sides of equal length.

What is Perpendicular bisector?

A perpendicular bisector is a line that bisects another line segment at a right angle, through the intersection point.

Given,

The perpendicular bisector of one side of a triangle goes through the opposite vertex

Consider the figure,

AX=BX ( bisection of the side)

CX=CX (Common side)

∠AXC=∠BXC=90 degrees

Therefore ΔAXC and ΔBXC are congruent.

Therefore AC = BC

Therefore, ΔABC is isosceles

Hence, if the perpendicular bisector of one side of a triangle goes through the opposite vertex, then is the triangle is always isosceles

Learn more about Isosceles triangle and Perpendicular bisector here

https://brainly.com/question/2264522

#SPJ2