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Lesson 4.1 Section 4.1: Apply Triangle Sum Properties ~ 10.8.09 In Your Notes, draw the pictures and classify the following triangles (by sides): ~ Isosceles ~ Equilateral ~ Scalene ~ 1 Lesson 4.1 In Your Notes, draw the pictures and classify the following triangles (by sides): ~ Isosceles ~ Equilateral ~ Scalene ~ scalene triangle ‐ No Congruent Sides isosceles triangle ‐ At least 2 Congruent Sides equilateral triangle ‐ All 3 sides are Congruent 2 Lesson 4.1 In Your Notes, draw the pictures and classify the following triangles (by angles): ~ Right triangle ~ Acute Triangle ~ ~Equiangular Triangle ~ Obtuse Triangle ~ 3 Lesson 4.1 In Your Notes, draw the pictures and classify the following triangles (by angles): ~ Right triangle ~ Acute Triangle ~ ~Equiangular Triangle ~ Obtuse Triangle ~ Acute Triangle (3 Acute Angles) Obtuse Triangle (1 Obtuse Angle) Equiangular Triangle (3 Congruent Angles) Right Triangle (1 Right Angle) 4 Lesson 4.1 Interior angles vs Exterior angles which angles are which? 5 Lesson 4.1 Interior angles: the original angles formed inside the three sides 6 Lesson 4.1 Exterior angles: angles that form linear pairs with the interior angles 7 Lesson 4.1 Exterior angles: angles that form linear pairs with the interior angles What about these? 8 Lesson 4.1 The Triangle Sum Theorem (Theorem 4.1): The sum of the interior B angles of any triangle is 180o C A m A+m B+m C = 180o OR orange angle + green angle + purple angle = 180o 9 Lesson 4.1 Exterior Angle Theorem (Theorem 4.2): The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles B C 1 A REMINDER exterior angle: make a linear pair with the interior angles . adjacent: next to. ‐‐> So nonadjacent: NOT next to . interior angle: angles formed inside the three sides 10 Lesson 4.1 Theorem 4.2: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles B C 1 m B+m A C=m 1 11 Lesson 4.1 A corollary (to a theorem) is a statement that can be proved easily using the theorem. Corollary(to the Triangle Sum Theorem ‐ 4.1): The acute angles of a right triangle are complementary C A B m A + m B = 90o 12 Lesson 4.1 TRIANGLE ACTIVITY!! yes, this took a long time and yes it was unnecessary 13 Lesson 4.1 B A C because we love activities 14 Lesson 4.1 B A C 15 Lesson 4.1 B B A A C C 16 Lesson 4.1 B B C A A C 17 Lesson 4.1 B B C A C 18 Lesson 4.1 B Example 3, pg. 87 (guides) (3x 9) o 73o D C xo A 19 Lesson 4.1 J Example 3, pg. 219 (books) xo 70o L (2x 5)o K M 20 Lesson 4.1 Miss Willson's Homework Policy 21 Lesson 4.1 Homework pg 221 (1‐7, *14‐19, 21‐26, 31‐34) *If you can show me that you can do 15, 16, and 18 correctly, then you don't need to do the other three problems! . ~You must show ALL of your work in all three problems in order for 14, 17 and 19 to be excused. ~it's okay if they are out of order on your homework 22