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4.1 Triangles and Angles

4.1 Triangles and Angles. Essential Question:. How do you classify triangles by the angles and their sides? How do you find the measures of their angles?. Definition: Triangle. A triangle is a figure formed by three segments joining three noncollinear points . Classification by Sides.

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4.1 Triangles and Angles

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  1. 4.1 Triangles and Angles

  2. Essential Question: • How do you classify triangles by the angles and their sides? • How do you find the measures of their angles?

  3. Definition: Triangle A triangle is a figure formed by three segments joining three noncollinear points.

  4. Classification by Sides Equilateral Triangle = 3 congruent sides Isosceles Triangle = At least 2 congruent sides Scalene Triangle = No congruent sides

  5. Classification by Angles Acute Triangle = 3 Acute Angles Equiangular Triangle = 3 congruent angles Right Angle = 1 Right Angle Obtuse Angle = 1 Obtuse Angle

  6. Example 1: Classifying Triangles When you classify a triangle, you need to be as specific as possible. “Triangle ABC” Acute Scalene

  7. Example 2: Classifying Triangles Obtuse Isosceles

  8. Example 3: Classifying Triangles Equiangular Equilateral

  9. Vertex A Side opposite Adjacent sides Vertex B Vertex C

  10. Right and Isosceles Triangles Leg Leg Hypotenuse Leg Base Leg

  11. By extending the sides we create Interior and Exterior Angles Interior Angles

  12. By extending the sides we create Interior and Exterior Angles Exterior Angles Exterior angles are adjacent to interior angles!

  13. Triangle Sum Theorem • The sum of the measure of the interior angles of a triangle is

  14. What is an Auxiliary Line ? To prove some theorems, you may need to add a line, segment, or ray to a diagram !!!

  15. 4 2 5 Given 1 3 Prove: 1. Draw a line through vertex 2 parallel to the base Parallel Postulate Theorem Angle Addition & Straight Angle Alternate Interior Angles Definition Congruent Angles Substitution Property of Equality

  16. Exterior Angle Theorem • The measure of an exterior angle of a triangle is equal to the sum of the measures of the 2 nonadjacent interior angles B 1 A C

  17. Finding an Angle Measure 65° (2x+10)° x° Exterior Angles Theorem X + 65 = 2X+10 Solve for X X = 55

  18. Corollary – a statement that can be easily proved using the theorem. • Corollary to the Triangle Sum Theorem: The acute angles of a right triangle are complementary A B

  19. Assignment • P199: 10 – 26, 31-39, 42, 47

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