5VocabularyTriangle Sum Theorem- The sum of the measures of the angles of a triangle is 180◦
6VocabularyCorollary to the Triangle Sum Theorem- The acute angles of a right triangle are complementary.
7VocabularyExterior Angle Theorem- The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.
8VocabularyLegs- The congruent sides of an isosceles triangles. Base- The other side of an isosceles triangle Base Angles- Two angles at the base of the triangle.
9VocabularyBase Angles Theorem- If two sides of a triangle are congruent, then the angles opposite them are congruent Converse of the Base Angles Theorem- If two angles of a triangle are congruent, then the opposite sides are congruent. Equilateral Theorem- If a triangle is equilateral, then it is equiangular. Equiangular Theorem- If a triangle is equiangular, then it is equilateral.
10Practice Find the value of x, and the measure of <C x C 2x x + 5 10 40º2xx + 510
11VocabularyPythagorean Theorem- a² + b² = c² Legs- The sides that form the right angle. Hypotenuse- The side opposite of the right angle. Distance Formula-
12PracticeFind the value of the unknown side length.12ac1177
13VocabularyConverse of the Pythagorean Theorem- If the square of the length of the longest side is equal to the sum of the squares on the legs, then the triangle is a right triangle. If c² < a² + b², then the triangle is acute If c² = a² + b², then the triangle is right. If c² > a² + b², then the triangle is obtuse.
14Practice Classify the triangles as acute, right or obtuse. 8 15 8 17 5 1321518
15VocabularyMedian of a Triangle- A segment from a vertex to the midpoint of the opposite side. Intersection of Medians of a Triangle- Medians of a triangle intersect at the centroid. The centroid is two thirds of the distance from each vertex to the midpoint of the opposite side.
17VocabularyTriangle Inequalities The side opposite of the largest angle, will be the longest side. The side opposite of the smallest angle, will be the shortest side. The angle opposite of the largest side, will be the largest angle. The angle opposite of the smallest side, will be the smallest angle.
18VocabularyTriangle Inequality- The sum of the lengths of any two sides of a triangle is greater than the third side. If a + b < c, then it does not form a triangle If a + b = c, then the lengths do not form a triangle. If a + b > c, a + c > b and c + b > a, then the lengths form a triangle.
19Practice Determine if the lengths form a triangle. 5, 11, 21 5, 16, 17 2, 3, 5