§21. The concept of quadrilaterals

A Grade 8 topic in Geometry: “§21. The concept of quadrilaterals” (pp. 103–105, I. B. Bekboev, A. A. Borubaev, A. A. Ayylchiev). Definition: a quadrilateral is a figure made of four points, no three of which lie on one straight line, and the four segments joining those points in pairs. In the quadrilateral ABCD the points A, B, C, D are its vertices, AB, BC, CD, DA are its sides, and ∠ABC, ∠BCD, ∠CDA, ∠DAB are its angles. The segments joining opposite vertices (AC, BD) are called diagonals. If, when a straight line is drawn through any side of a quadrilateral, the quadrilateral lies in one of the half-planes into which that line divides the plane, the quadrilateral is convex; otherwise it is non-convex. The sum of the sides of a quadrilateral is called its perimeter. By Theorem 34 the sum of the interior angles of a quadrilateral is 360°: a diagonal divides it into two triangles, and the interior angles of each triangle add up to 180°.