The midpoint theorem, midsegment theorem, or midline theorem states that if the midpoints of two sides of a triangle are connected, then the resulting...

The butterfly theorem is a classical result in Euclidean geometry, which can be stated as follows:: p. 78  Let M be the midpoint of a chord PQ of a circle...

Midpoint theorem may refer to the following mathematical theorems: Midpoint theorem (triangle) Midpoint theorem (conics) Midpoint theorem, describing...

and passing through its midpoint also passes through the circle's center. The butterfly theorem states that, if M is the midpoint of a chord PQ of a circle...

Every triangle has a unique Steiner inellipse which is interior to the triangle and tangent at the midpoints of the sides. Marden's theorem shows how...

A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular...

from the apex to the midpoint of the base, the perpendicular bisector of the base within the triangle, the segment within the triangle of the unique axis...

triangle A B C {\textstyle ABC} , construct squares on any two adjacent sides, for example A C {\textstyle AC} and B C {\textstyle BC} . The midpoint...

planar or not. The theorem can be generalized to the midpoint polygon of an arbitrary polygon. Referring to the diagram above, triangles ADC and HDG are...

In geometry, Apollonius's theorem is a theorem relating the length of a median of a triangle to the lengths of its sides. It states that the sum of the...

derived from the formula of an isosceles triangle by Pythagoras theorem: the altitude h {\displaystyle h} of a triangle is the square root of the difference...

(geometric mean theorem; see special cases, inverse Pythagorean theorem) For acute triangles, the feet of the altitudes all fall on the triangle's sides (not...

intersection of the line EM and the edge AD. Then, the theorem states that F is the midpoint AD. We need to prove that AF = FD. We will prove that both...

a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three...

triangle ABC with side length 2 and with point M as the midpoint of segment BC. Draw an altitude line from A to M. Then ABM is a 30°–60°–90° triangle...

In geometry, the theorem that the angles opposite the equal sides of an isosceles triangle are themselves equal is known as the pons asinorum (/ˈpɒnz...

general form a triangle, and the Gauss–Lucas theorem states that the roots of its derivative lie within this triangle. Marden's theorem states their location...

the midpoint theorem of triangles and Heron's formula. The orthocenter of the medial triangle coincides with the circumcenter of the original triangle. The...

The exterior angle theorem is Proposition 1.16 in Euclid's Elements, which states that the measure of an exterior angle of a triangle is greater than either...

The centroid of a triangle is the intersection of the three medians of the triangle (each median connecting a vertex with the midpoint of the opposite side)...

The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry...

the incenter–excenter lemma is the theorem that the line segment between the incenter and any excenter of a triangle, or between two excenters, is the...

the three excircles of the triangle as well as its incircle. A very short proof of this theorem based on Casey's theorem on the bitangents of four circles...

equilateral triangle. The three-circle construction may be performed with a compass alone, not even needing a straightedge. By the Mohr–Mascheroni theorem the...

of in terms of a geodesic triangle Δ = zγ(0)γ(1). The left-hand side is the square distance from the vertex z to the midpoint of the opposite side. The...

triangle. It is so named because it passes through nine significant concyclic points defined from the triangle. These nine points are: The midpoint of...

angles; the area T of the triangle; the medians ma, mb, and mc of the sides (each being the length of the line segment from the midpoint of the side to the opposite...

In spherical geometry, Lexell's theorem holds that every spherical triangle with the same surface area on a fixed base has its apex on a small circle...

that B is the midpoint of line segment AC. Construct point D as the intersection of circles A(B) and B(A). (∆ABD is an equilateral triangle.) Construct...

than 2%. A cleaver of a triangle is a line segment that bisects the perimeter of the triangle and has one endpoint at the midpoint of one of the three sides...