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DO NOW

DO NOW. 30 + 90 + X = 180 55 + X + 105 = 180 X + 58 = 90 31 + X = 90. Triangles, Triangles, and MORE Triangles. Geometry Week 7 of 9 Unit 2: Angles and Angle Relationships. Standards & Objectives. Standard 12.0 and 13.0 Objectives:

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DO NOW

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  1. DO NOW 30 + 90 + X = 180 55 + X + 105 = 180 X + 58 = 90 31 + X = 90

  2. Triangles, Triangles, and MORE Triangles Geometry Week 7 of 9 Unit 2: Angles and Angle Relationships

  3. Standards & Objectives Standard 12.0 and 13.0 Objectives: To classify triangles and find the measures of their angles To use exterior angles of triangles

  4. ACTIVITY Draw and cut out a large triangle. Number the angles and tear them off. Place the three angles adjacent to each other to form one angle. 1) What kind of angle is formed by the three smaller angles? What is its measure? 2) Make a conjecture about the sum of the measures of the angles of a triangle.

  5. Triangle Angle-Sum Theorem The sum of the measures of the angles of a triangle is 180.

  6. Different Types of Triangles • There are several different types of triangles. • You can classify a triangle by its sides and its angles. • There are THREE different classifications for triangles based on their sides. • There are FOUR different classifications for triangles based on their angles.

  7. Classifying Triangles by Their Sides • EQUILATERAL– 3 congruent sides • ISOSCELES – at least two sides congruent • SCALENE – no sides congruent

  8. Classifying Triangles by Their Angles • EQUIANGULAR – all angles are congruent • ACUTE – all angles are acute • RIGHT – one right angle • OBTUSE – one obtuse angle EQUIANGULAR ACUTE RIGHT OBTUSE

  9. Can You Classify the Different Triangles in the Picture Below? Classify the following triangles: AED, ABC, ACD, ACE

  10. The Classifications… • Triangle AED = Equilateral, Equiangular • Triangle ABC = Equilateral, Equiangular • Triangle ACD = Scalene, Obtuse • Triangle ACE = Scalene, Right • So how did you do?

  11. Triangle Exterior Angle Theorem 2 1 3 The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

  12. EXAMPLE 40 30 X Measure of X = 40 + 30 Measure of X = 70

  13. PRACTICE

  14. EXAMPLE X 113 70 113 = 70 + Measure of X 43 = Measure of X

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