2-5 Notes
... • Two angles whose measures have a sum of 180°. Each angle is called the supplement of the other. ...
... • Two angles whose measures have a sum of 180°. Each angle is called the supplement of the other. ...
Activity 3.5.4 Properties of Parallelograms
... You have been investigating properties of the different quadrilaterals. In this activity we will prove some properties of parallelograms. First let’s review the definition and properties that we investigated already. 1. A parallelogram is defined as a quadrilateral with two pairs of ________________ ...
... You have been investigating properties of the different quadrilaterals. In this activity we will prove some properties of parallelograms. First let’s review the definition and properties that we investigated already. 1. A parallelogram is defined as a quadrilateral with two pairs of ________________ ...
Geometry lectures
... Proof. Through each of the vertices of the triangle ABC we draw a parallel to the opposite side. By intersecting these lines we get another triangle A′ B ′ C ′ , such that A ∈ B ′ C ′ , B ∈ A′ C ′ , C ∈ A′ B ′ . The proof is based on the observation that the altitudes in the triangle ABC are perpend ...
... Proof. Through each of the vertices of the triangle ABC we draw a parallel to the opposite side. By intersecting these lines we get another triangle A′ B ′ C ′ , such that A ∈ B ′ C ′ , B ∈ A′ C ′ , C ∈ A′ B ′ . The proof is based on the observation that the altitudes in the triangle ABC are perpend ...
Riemann–Roch theorem
The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles. It relates the complex analysis of a connected compact Riemann surface with the surface's purely topological genus g, in a way that can be carried over into purely algebraic settings.Initially proved as Riemann's inequality by Riemann (1857), the theorem reached its definitive form for Riemann surfaces after work of Riemann's short-lived student Gustav Roch (1865). It was later generalized to algebraic curves, to higher-dimensional varieties and beyond.