AMSCO'S Geometry. New York - Rye High School

368 Parallel LinesA convex polygon is a polygon inwhich each of the interior angles measuresless than 180 degrees. Polygon PQRST is aconvex polygon and a pentagon. A concavepolygon is a polygon in which at leastone interior angle measures more than180 degrees. Polygon ABCD is a concavepolygon and a quadrilateral. In the rest ofthis textbook, unless otherwise stated, allpolygons are convex.TPSQRACDBInterior Angles of a PolygonA pair of angles whose vertices are the endpoints of a common side arecalled consecutive angles. And the vertices of consecutive angles are calledconsecutive vertices or adjacent vertices. For example, in PQRST, P and Qare consecutive angles and P and Q are consecutive or adjacent vertices.Another pair of consecutive angles are T and P. Vertices R and T are nonadjacentvertices.A diagonal of a polygon is a line segmentwhose endpoints are two nonadja-DEcent vertices. In hexagon ABCDEF, theCvertices adjacent to B are A and C andthe vertices nonadjacent to B are D, E,Fand F. Therefore, there are three diagonalswith endpoint B: BD, BE, and BF.ABThe polygons shown above have four, five, and six sides. In each polygon, allpossible diagonals from a vertex are drawn. In the quadrilateral, two trianglesare formed. In the pentagon, three triangles are formed, and in the hexagon,four triangles are formed. Note that in each polygon, the number of trianglesformed is two less than the number of sides.• In a quadrilateral: the sum of the measures of the angles is 2(180) 360.• In a pentagon: the sum of the measures of the angles is 3(180) 540.• In a hexagon: the sum of the measures of the angles is 4(180) 720.