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Geometry Chapter 4 Key Vocabulary Triangle – polygon with three sides Vertex – each of the three points joining the sides of the triangle Adjacent Sides – two sides sharing a common vertex Right Triangle – triangle with one right angle Legs – adjacent sides that form the right angle Hypotenuse – side opposite the right angle Isosceles Triangle – triangle with at least two congruent sides Legs – the congruent sides of an isosceles triangle Base – the third side of an isosceles triangle Interior Angles Exterior Angles Congruent Triangles – when the corresponding sides and angles of each triangle are congruent Congruence Statement – states that polygons are congruent CPCTC – Corresponding Parts of Congruent Triangles are Congruent Base Angles – the angles adjacent to the base Vertex Angle – the angle opposite the base 1 Geometry Chapter 4 Postulates/ Theorems Theorem 4.1 – Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180 Theorem 4.2 – Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles Corollary to the Triangle Sum Theorem The acute angles of a right triangle are complementary Theorem 4.3 – Third Angles Theorem If two angles of one triangle are congruent to two triangles of another triangle, then the third angles are also congruent. Theorem 4.4 – Properties of Congruent Triangles B Reflexive Property of Congruent Triangles Every triangle is congruent to itself A E Symmetric Property of Congruent Triangles If ABC DEF , then DEF ABC C D Transitive Property of Congruent Triangles F K If ABC DEF and DEF JKL , then ABC JKL J L Postulate 19 – Side-Side-Side (SSS) Congruence Postulate If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent 2 Geometry Chapter 4 Postulate 20 – Side-Angle-Side (SAS) Congruence Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent Theorem 4.5 – Hypotenuse-Leg (HL) Congruence Theorem If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent Postulate 21 – Angle-Side-Angle (ASA) Congruence Postulate If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent Theorem 4.6 – Angle-Angle-Side (AAS) Congruence Theorem If two angles and the non-included side are congruent to two angles and the non-included side of another triangle, then the two triangles are congruent Theorem 4.7 – Base Angle Theorem If two sides of a triangle are congruent, then the angles opposite them are congruent Theorem 4.8 – Converse to the Base Angle Theorem If two angles of a triangle are congruent, then the sides opposite them are congruent Corollary to the Base Angle Theorem If a triangle is equilateral, then it is equiangular 3 Geometry Chapter 4 Corollary to the Converse of the Base Angle Theorem If a triangle is equiangular, then it is equilateral Concepts Classification by Sides Equilateral Isosceles Scalene Classification by Angles Acute Right Obtuse Equiangular Ways to Prove Triangle Congruent SSS SAS ASA AAS HL 4