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Transcript

Section 4.1 ~ Triangle Sum Properties Topics in this lesson: • classification of triangles • Triangle Sum Theorem • Exterior Angle Theorem • interior & exterior angles • corollary Classifying Triangles by Sides Scalene Triangle Isosceles Triangle Equilateral Triangle No ≅ sides At least 2 ≅ sides 3 ≅ sides Classifying Triangles by Angles Acute Triangle 3 acute angles Right Triangle 1 right angle Obtuse Triangle 1 obtuse angle Equiangular Triangle 3 ≅ angles Example 1 Draw an isosceles right triangle. Draw an obtuse scalene triangle. . 4.1 1 Example 2 Classify RST by its sides. Then determine if the triangle is a right triangle. Step 1: Find the lengths of the sides. RT = RS = ST = Step 2: Check slopes for a right angle. RT = ST = Classification: Always be as specific as you can. If you can classify by angles AND sides, do so. Vocabulary interior angle interior angles the original inside angles when the sides of a polygon are extended exterior angle exterior angles the angles that form linear pairs with the interior angles when the sides of a polygon are extended 4.1 2 Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180o. 180o 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. Example 3 Use the diagram at the right to find the measure of DCB. Example 4 Find the measure of 1 in the diagram. 4.1 3 Vocabulary corollary to a theorem a statement that usually follows a theorem that can be proven easily using a theorem Corollary to the Triangle Sum Theorem The acute angles of a right triangle are complementary. 90o Example 5 The front face of the wheelchair ramp shown forms a right triangle. The measure of one acute angle in the triangle is eight times the measure of the other. Find the measure of each acute angle. What is the measure of the obtuse angle formed between the ramp and a segment extending from the horizontal leg? 4.1 4