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Mastering Angle Relationships: Essential Learnings & Vocabulary

Understand, measure, & classify angles. Identify congruent, special pairs. Use protractor to measure angles. Discover acute, right, obtuse angles. Learn angle bisector, perpendicular lines. Examples & vocabulary like adjacent, complementary angles.

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Mastering Angle Relationships: Essential Learnings & Vocabulary

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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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