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: Special Lines

Description

This lecture covers the geometry of a triangle, including medians, mediatrices, and altitudes. It explains how medians connect a vertex to the midpoint of the opposite side, how mediatrices intersect at the circumcenter, and how altitudes pass through a vertex and are perpendicular to the opposite side.

Official source

Ontological neighbourhood

Mathematics

Geometry: Euclidean geometry

Related concepts (32)

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.

Medial triangle

In Euclidean geometry, the medial triangle or midpoint triangle of a triangle △ABC is the triangle with vertices at the midpoints of the triangle's sides AB, AC, BC. It is the n = 3 case of the midpoint polygon of a polygon with n sides. The medial triangle is not the same thing as the median triangle, which is the triangle whose sides have the same lengths as the medians of △ABC. Each side of the medial triangle is called a midsegment (or midline). In general, a midsegment of a triangle is a line segment which joins the midpoints of two sides of the triangle.

Altitude (triangle)

In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the the side opposite the vertex. This line containing the opposite side is called the extended base of the altitude. The intersection of the extended base and the altitude is called the foot of the altitude. The length of the altitude, often simply called "the altitude", is the distance between the extended base and the vertex. The process of drawing the altitude from the vertex to the foot is known as dropping the altitude at that vertex.

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.

Circumcircle

In geometry, the circumscribed circle or circumcircle of a triangle is a circle that passes through all three vertices. The center of this circle is called the circumcenter of the triangle, and its radius is called the circumradius. The circumcenter is the point of intersection between the three perpendicular bisectors of the triangle's sides, and is a triangle center. More generally, an n-sided polygon with all its vertices on the same circle, also called the circumscribed circle, is called a cyclic polygon, or in the special case n = 4, a cyclic quadrilateral.

Related lectures (28)

Triangle Resolution: Trigonometry Basics

Covers the resolution of triangles using trigonometric functions to find missing sides and angles.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

Mediatrix and Bisector

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

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Elementary Operations in Geometry