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math424jan7.notebook January 07, 2014 hw due Wed. Bumby p. 156# 210 challenge 1 p. 159 written 123 odd Jurgenson p. 97 # 8,9,10, 14,15,16,23,24 We will have an assessment Monday January 27. Happy 2014 Theorem: the sum of the measures of the angles of a triangle is 180 degrees. A corollary is a theorem that follows easily from another theorem. B The angle formed by the extension of one side of a triangle and a side of the triangle is called an exterior angle of the triangle. A C D Angle BCD is an exterior angle of triangle ABC. Angles A and B are called the remote interior angles. Any side can be extended to form exterior angles of the triangle. (or any polygon for that matter) Theorem: (exterior angle theorem) The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles. Corollaries to "The sum of the measures of the angles of a triangle is 180 degrees" If 2 angles in one triangle are congruent to 2 angles in another triangle, then the third angles are congruent. In a triangle, there can be no more than one right angle or one obtuse angle. The acute angles of a right triangle are complementary. Each angle of an equiangular triangle is 60 degrees. 1 math424jan7.notebook January 07, 2014 2 math424jan7.notebook January 07, 2014 Identify exterior angles in the diagram below, use the exterior angle theorem to show the relationship between the angle and its remote interior angles. 8 C 7 6 B 3 math424jan7.notebook January 07, 2014 A polygon is a closed figure made of coplanar segments (called sides) so that each segment intersects exactly 2 other segments, one at each endpoint and no two segments with a common endpoint are collinear. A convex polygon is a polygon such that no line containing a side of the polygon contains a point in the interior of the polygon. A segment joining 2 nonconsecutive vertices is called a diagonal of the polygon Regular polygon: a polygon that is equiangular and equilateral. 4