In another problem, we saw that in an isosceles triangle, the height to the base from the apex is also the angle bisector. Here, we will show the opposite: that the angle bisector is perpendicular to … [Read more...] about Angle bisector is perpendicular to the base in an isosceles triangle

# Isosceles Triangle

A triangle in which two of the sides are equal is called an “Isosceles triangle”, and we often identify the equal side by tagging them with a short line:

The third side is called the "base", and we will prove that the angels at the two sides of the base (and opposite the two equal sides) are congruent.

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*Now that we've explained the basic concept of isosceles triangles in geometry, let's scroll down to work on specific geometry problems relating to this topic.*

## Converse Base Angle Theorem

In today's lesson, we will prove the converse to the Base Angle theorem - if two angles of a triangle are congruent, the triangle is isosceles. We will use congruent triangles for the proof. From … [Read more...] about Converse Base Angle Theorem

## Angle Bisector in a Triangle

Today's geometry problem presents an application of the angle bisector theorem in a triangle. It also incorporates several other concepts we've explored, like the properties of isosceles triangles and … [Read more...] about Angle Bisector in a Triangle

## Converse Angle Bisector Theorem for Isosceles Triangles

In today's lesson, we will prove the Converse Angle Bisector Theorem for Isosceles Triangles. We'll show that if a triangle's angle bisector is perpendicular to the opposite side, the triangle is an … [Read more...] about Converse Angle Bisector Theorem for Isosceles Triangles

## Isosceles Triangles: the Median to the Base is Perpendicular to the Base

In a triangle, a line that connects one corner (or vertice) to the middle point of the opposite side is called a median. A property of isosceles triangles, which is simple to prove using triangle … [Read more...] about Isosceles Triangles: the Median to the Base is Perpendicular to the Base

## Isosceles Triangles: the Height to the Base Bisects the Apex Angle

We can use the proof that in isosceles triangles the height to the base bisects the base, and get a "two-for-one," as the exact same proof shows us multiple corresponding parts that are … [Read more...] about Isosceles Triangles: the Height to the Base Bisects the Apex Angle

## The Height to the Base of an Isosceles Triangle Bisects the Base

In today's lesson we'll learn a simple strategy for proving that in an isosceles triangle, the height to the base bisects the base. Having proven the Base Angles Theorem for isosceles triangles … [Read more...] about The Height to the Base of an Isosceles Triangle Bisects the Base

## Base Angles Theorem

In this lesson, we will show you how to easily prove the Base Angles Theorem: that the base angles of an isosceles triangle are congruent. We will prove most of the properties of special triangles … [Read more...] about Base Angles Theorem