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Angle Relationships

Angle Relationships. Notes 3 – Section 1.5. Essential Learnings. Students will understand and be able to measure and classify angles. Students will be able to identify and use congruent and special pairs of angles. Students will be able to identify perpendicular lines. Measures of Angles.

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Angle Relationships

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  1. Angle Relationships Notes 3 – Section 1.5

  2. Essential Learnings • Students will understand and be able to measure and classify angles. • Students will be able to identify and use congruent and special pairs of angles. • Students will be able to identify perpendicular lines.

  3. Measures of Angles • Angles are measured in degrees. Use your protractor to measure angles.

  4. Classifying Angles Acute angle Right angle Obtuse angle m∠A< 90⁰ m∠A= 90⁰ 90⁰<m∠A <180⁰ A A A

  5. Copying an Angle • Use your compass.

  6. Angle Bisector • Angle bisector – a ray that divides an angle into two congruent angles. C ∠ABC ≅ ∠CBD 70⁰ 70⁰ A D B

  7. Constructing Angle Bisector • Use your compass.

  8. Example 3 Ray QS bisects ∠PQT. m∠PQT=60⁰ andm∠PQS=4x+14, solve for x. m∠PQS = ½m∠PQT 4x+14= ½ (60) 4x+14 = 30 T 4x = 16 S x = 4 P Q R

  9. Example 4 Ray KM bisects ∠NKL. m∠MKL=3x+13 andm∠NKM=6x-2, m∠NKL=? m∠MKL = 3x+13 m∠MKL = m∠NKM m∠MKL = 3(5)+13 3x+13= 6x-2 m∠MKL = 28 15 = 3x N 5 = x m∠NKL = 2(28) x = 5 m∠NKL = 56° M J K L

  10. Angle Relationships Notes 3 – Section 1.5

  11. Vocabulary • Adjacent angles – two angles that have a common vertex and a common side. • Linear pair of angles – two adjacent angles that sum to 180⁰.

  12. Vocabulary • Vertical angles – two nonadjacent angles formed by two intersecting lines. • Vertical angles are congruent.

  13. Vocabulary • Complementary angles – two angles whose sum is 90⁰. • Supplementary angles – two angles whose sum is 180⁰.

  14. Vocabulary • Perpendicular lines – lines that meet at 90⁰.

  15. Example 5 • Find the value of the variable. 2x+(4x+108) = 180 6x+108 = 180 2x 4x+108 6x = 72 x = 12

  16. Example 6 • Find the value of each variable. 6y-84 = 2y+8 4y = 92 y = 23 6y-84 3x 2y+8 2y+8+3x = 180 2(23)+8+3x = 180 54+3x = 180 3x =126 x = 42

  17. Assignment Page 41-44: 20-25, 37-41 odd, 64, 65 Page 51: 9-25 odd

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