Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Triangle Geometry: Examples

Description

This lecture covers examples of determining the area of a triangle and finding the equations of the perpendicular bisector of a side and the angle bisectors. It also explores the concept of the incenter of a triangle.

Official source

Ontological neighbourhood

Mathematics

Geometry: Euclidean geometry

Related concepts (32)

Incenter

In geometry, the incenter of a triangle is a triangle center, a point defined for any triangle in a way that is independent of the triangle's placement or scale. The incenter may be equivalently defined as the point where the internal angle bisectors of the triangle cross, as the point equidistant from the triangle's sides, as the junction point of the medial axis and innermost point of the grassfire transform of the triangle, and as the center point of the inscribed circle of the triangle.

Bisection

In geometry, bisection is the division of something into two equal or congruent parts (having the same shape and size). Usually it involves a bisecting line, also called a 'bisector'. The most often considered types of bisectors are the 'segment bisector' (a line that passes through the midpoint of a given segment) and the 'angle bisector' (a line that passes through the apex of an angle, that divides it into two equal angles). In three-dimensional space, bisection is usually done by a bisecting plane, also called the 'bisector'.

Triangle

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted . In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane (i.e. a two-dimensional Euclidean space). In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane.

Angle bisector theorem

In geometry, the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle. Consider a triangle △ABC. Let the angle bisector of angle ∠ A intersect side at a point D between B and C.

Perpendicular

In elementary geometry, two geometric objects are perpendicular if their intersection forms right angles (angles that are 90 degrees or π/2 radians wide) at the point of intersection called a foot. The condition of perpendicularity may be represented graphically using the perpendicular symbol, ⟂. Perpendicular intersections can happen between two lines (or two line segments), between a line and a plane, and between two planes.

Related lectures (30)

Triangle Geometry: Special Lines (Part 2)

Explores triangle bisectors, locus of equidistant points, and incenter intersection.

Elementary Operations in Geometry

Explores elementary operations in geometry, including addition, subtraction, multiplication, and division of segments and angles.

Mediatrix and Bisector

Explores the mediatrix and bisector properties in right-angled triangles through proofs and constructions.

Angle at the Center & Power of a Point

Explores angles at the center of a circle and the power of a point relative to a circle, emphasizing their importance in geometry and CAD software.

Triangle Resolution: Trigonometry Basics