Geometry Chapter 4 Cipollone

Vocabulary Triangle- a figure formed by three segments joining three non-collinear points. A triangle can be classified by sides or angles.

Re-teach Equilateral Triangle- Isosceles Triangle- Scalene Triangle-

Practice

Vocabulary Triangle Sum Theorem- The sum of the measures of the angles of a triangle is 180◦

Vocabulary Corollary to the Triangle Sum Theorem- The acute angles of a right triangle are complementary.

Vocabulary Exterior 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.

Vocabulary Legs- 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.

Vocabulary Base 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.

Practice Find the value of x, and the measure of <C x C 2x x + 5 10 40º 2x x + 5 10

Vocabulary Pythagorean Theorem- a² + b² = c² Legs- The sides that form the right angle. Hypotenuse- The side opposite of the right angle. Distance Formula-

Practice Find the value of the unknown side length. 12 a c 11 7 7

Vocabulary Converse 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.

Practice Classify the triangles as acute, right or obtuse. 8 15 8 17 5 13 2 15 18

Vocabulary Median 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.

Practice Draw the medians for each side/angle.

Vocabulary Triangle 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.

Vocabulary Triangle 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.

Practice Determine if the lengths form a triangle. 5, 11, 21 5, 16, 17 2, 3, 5