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1.4 Measure and Classify Angles

1.4 Measure and Classify Angles . You will name, measure and classify angles. Classifying Angles. Acute angle : between 0 and 90 Right angle : exactly 90 degrees Symbol: Obtuse Angle : between 90 and 180 Straight angle : exactly 180 degrees. Angles. Naming Angles

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1.4 Measure and Classify Angles

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  1. 1.4 Measure and Classify Angles You will name, measure and classify angles.

  2. Classifying Angles • Acute angle: between 0 and 90 • Right angle: exactly 90 degrees • Symbol: • Obtuse Angle: between 90 and 180 • Straight angle: exactly 180 degrees

  3. Angles • Naming Angles • Use 3 capital letters – Vertex in the middle • Can use one capital letter if it is the vertex and it is obvious which angle you are referring to • Can use the number located inside the angle • Angle Bisector • Divides the angle into 2 congruent parts

  4. Naming angles • Name this angle three different ways

  5. Naming angles • Name this angle three different ways

  6. Naming angles • Name this angle four different ways

  7. Name this angle in 4 ways

  8. Congruent Angles • Have the same angle measure

  9. Congruent Angles • Can be marked using the same number of hash marks. H W F Q

  10. Angle Addition Postulate • Smaller angles can be added together to form larger angles if they share a common vertex.

  11. Given that the m<LKN=145⁰, find the m<LKM and m<MKN

  12. Find the indicated angle measures. 3. Given that <KLMis a straight angle, find x andm<NLM. for Example 3 GUIDED PRACTICE

  13. 4. Given that < EFGis a right angle, find x andm<HFG. for Example 3 GUIDED PRACTICE

  14. Homework • Page 28 # 4 – 40 even • Honors: also # 42, 44, 48, 49, 50

  15. Use the diagram to find the measure of the indicated angle. Then classify the angle. a.KHJ b.GHK c.GHJ d.GHL EXAMPLE 2 Measure and classify angles SOLUTION A protractor has an inner and an outer scale. When you measure an angle, check to see which scale to use.

  16. Angle Addition Postulate • When two angles share a ray, a Part+ Part = Whole or Little + Little = Big • Very similar to segment addition Postulate

  17. Congruent Angles • Angles that have the same measure • Angle measures are equal: m<A=m<B • The measure of angle A is equal to the measure of angle B • Angle measures are congruent: <A <B • Angle A is congruent to angle B • When talking about measures, use equal sign. When talking about congruency, use congruent sign

  18. EXAMPLE 4 Identify congruent angles The photograph shows some of the angles formed by the ropes in a trapeze apparatus. Identify the congruent angles. If m<DEG = 157° ,what is m<GKL?

  19. Use the diagram shown. for Example 4 GUIDED PRACTICE 5. Identify all pairs of congruent angles in the diagram.

  20. Use the diagram shown. 6. In the diagram, m < PQR = 130 , m<QRS = 84, and m<TSR = 121 . Find the other angle measures in the diagram. for Example 4 GUIDED PRACTICE

  21. Angle • Formed by two rays that meet at an endpoint • Rays are considered sides of an angle • What is the vertex? What rays form the angle?

  22. Name the three angles in the diagram. Vertex of an Angle • Where the sides of an angle meet. • When naming an angle, vertex goes in the middle

  23. In the diagram at the right, YWbisects <XYZ, and m<XYW = 18. Find m<XYZ. Angle bisector A ray that divides an angle into two angles that are congruent (equal)

  24. Protractor Postulate • The rays of an angle can be matched one to one with real numbers from 0 to 180 • The measure of an angle is equal to the absolute value of the difference between the real number of the rays (much like the segment addition postulate)

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