We've seen that when a square is inscribed in a circle, we can express all the properties of either the square or circle (area, perimeter, circumference, radius, side length) if we know just the … [Read more...] about A Circle Inscribed in a Square

## Square Inscribed in a Circle

When a square is inscribed in a circle, we can derive formulas for all its properties- length of sides, perimeter, area and length of diagonals, using just the circle's radius. Conversely, we can … [Read more...] about Square Inscribed in a Circle

## Three Parallel Lines Theorem

The three parallel lines theorem is another theorem that provides a ratio between line segments created by a transversal of parallel lines, similar to the Intercept Theorem. It states that if three … [Read more...] about Three Parallel Lines Theorem

## Hinge Theorem

What is the Hinge Theorem? Let's say you have a pair of triangles with two congruent sides but a different angle between those sides. Think of it as a hinge, with fixed sides, that can be opened to … [Read more...] about Hinge Theorem

## Converse of the Scalene Triangle Inequality

In today's lesson, we will prove the converse of the scalene triangle inequality. Using proof by contradiction, we will show that the side facing the larger angle is longer. Having proven the … [Read more...] about Converse of the Scalene Triangle Inequality

## 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

## Perpendicular Bisector Theorem

In today's geometry lesson, we will show a fairly easy way to prove the perpendicular bisector theorem. A line that splits another line segment (or an angle) into two equal parts is called a … [Read more...] about Perpendicular Bisector Theorem

## Converse of the Angle Bisector Equidistant Theorem

In today's lesson, we will show how to prove the converse of the Angle Bisector Equidistant Theorem. The Angle Bisector Equidistant Theorem states that any point that is on the angle bisector is … [Read more...] about Converse of the Angle Bisector Equidistant Theorem