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Understanding Angles: Measurement, Classification, and Congruence (Lesson 1-2)

This comprehensive lesson focuses on measuring and classifying angles, including right, acute, and obtuse angles. Students will learn to identify and utilize congruent angles and angle bisectors. Key concepts include understanding the vocabulary related to angles and their parts, measuring angles accurately, and applying knowledge to solve problems. Through examples, learners will practice determining angle measures and relationships, fostering skills in geometry applicable to various real-world scenarios.

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Understanding Angles: Measurement, Classification, and Congruence (Lesson 1-2)

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  1. Splash Screen

  2. You measured line segments. (Lesson 1–2) • Measure and classify angles. • Identify and use congruent angles and the bisector of an angle. Then/Now

  3. degree • right angle • acute angle • obtuse angle • angle bisector • ray • opposite rays • angle • side • vertex • interior • exterior Vocabulary

  4. Answer: Angles and Their Parts A. Name all angles that have B as a vertex. Example 1

  5. Answer: Angles and Their Parts B.Name the sides of5. Example 1

  6. C. Angles and Their Parts Example 1

  7. A B C D A. B. C. D. A. Example 1a

  8. A B C D A. B. C. D. none of these B. Example 1b

  9. A B C D A. B. C. D. Which of the following is another name for 3? C. Example 1c

  10. Concept

  11. Measure and Classify Angles A. Measure TYV and classify it as right, acute, or obtuse. Answer:mTYV = 90, so TYV is a right angle. Example 2

  12. Measure and Classify Angles Example 2

  13. A B C D A.Measure CZD and classify it as right, acute, or obtuse. A. 30°, acute B. 30°, obtuse C. 150°, acute D. 150°, obtuse Example 2a

  14. A B C D B.Measure CZE and classify it as right, acute, or obtuse. A. 60°, acute B. 90°, acute C. 90°, right D. 90°, obtuse Example 2b

  15. Measure and Classify Angles INTERIOR DESIGN Wall stickers of standard shapes are often used to provide a stimulating environment for a young child’s room. A five-pointed star sticker is shown with vertices labeled. Find mGBH and mHCI if GBH  HCI, mGBH = 2x + 5, and mHCI =3x – 10. Example 3

  16. Measure and Classify Angles Step 1 Solve for x. GBH  HCI Given mGBH  mHCI Definition of congruent angles 2x + 5 = 3x – 10 Substitution 2x + 15 = 3x Add 10 to each side. 15 = x Subtract 2x from each side. Example 3

  17. . Measure and Classify Angles Step 2 Use the value of x to find the measure of either angle. Answer:mGBH = 35, mHCI = 35 Example 3

  18. A B C D Find mBHC and mDJE if BHC  DJE, mBHC = 4x + 5, and mDJE = 3x + 30. A.mBHC = 105, mDJE = 105 B.mBHC = 35, mDJE = 35 C.mBHC = 35, mDJE = 105 D.mBHC = 105, mDJE = 35 Example 3

  19. End of the Lesson

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