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Transcript
Chapter 5 Triangle properties C – 25 The sum of the measures of the angles of a triangle is 180° C - 26 If two angles of one triangle are equal in measure to two angles of another triangle, then the third angle in each triangle is equal. (Third angle Conjecture) Lesson 5.2 C – 27 If a triangle is isosceles, then its base angles are congruent. (Isosceles Triangle conjecture) C – 28 If a triangle has two congruent angles, then it is an isosceles triangle. (Converse of the Isosceles Triangle conjecture) C – 29 An equilateral triangle is equiangular and conversely, an equiangular triangle is equilateral. Lesson 5.3 C – 30 The sum of the lengths of any two sides of a triangle is greater than the length of the third side (Triangle Inequality conjecture) C – 31 In a triangle, the longest side is opposite the angle with the greatest measure and the shortest side is opposite the angle with the least measure. (Sideangle Inequality conjecture) C – 32 The measure of an exterior angle of a triangle is equal to the measures of the remote interior angles (Triangle Exterior Angle conjecture) m ABC = 50.27 m BAC = 69.41 A 50.27+69.41 = 119.68 m ACD = 119.68 B C D Lesson 5.4 C – 33 If the three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent. (SSS Congruent Conjecture) C – 34 If two sides and the angle between them in one triangle are congruent to two sides and the angle between them in another triangle, then the triangles are congruent. (SAS Congruent conjecture) Lesson 5.5 C – 35 If two angles and the side between them in one triangle are congruent to two angles and the side between them in another triangle, then the triangles are congruent. (ASA Congruent conjecture) C – 36 If two angles and a side that is not between them in one triangle are congruent to the corresponding two angles and side not between them in another triangle, then the triangles are congruent. (SAA Congruent conjecture) Lesson 5.6 CPCTC – Corresponding parts of congruent triangles are congruent. A Given: AR ER, EC AC Show: E A C B D 1. 1. Given 2. 2. Given 3 3 4 5 4 5 CPCTC Lesson 5.7 C – 37 In an isosceles triangle, the bisector of the vertex angle is also the altitude to the base and the median to the base. (Vertex Angle Bisector conjecture)