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Geometry

This geometry lesson focuses on proving angles congruent through various theorems, exploring definitions of vertical, adjacent, complementary, and supplementary angles. Theorems such as the Vertical Angles Theorem and Congruent Supplements Theorem will guide students in understanding the relationships between angles formed by intersecting lines. Practical examples and practice problems will reinforce concepts, allowing students to solve for unknown angles and demonstrate proofs. Engage with challenges to fortify your understanding of angles and their properties.

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Geometry

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  1. Geometry • Agenda 1. ENTRANCE 2. go over Practice 1-6 3. 2-5 Proving Angles Congruent 4. Practice Assignment 5. EXIT

  2. Chapter 1 2-5 Proving Angles Congruent

  3. Vertical Angles • Opposite angles formed by intersecting lines The opposite angles are _______ and _______.

  4. Adjacent Angles • Angles that are beside each other and share a ray

  5. Complementary Angles • Angles whose sum is 90º 1 and 2 are complementary.

  6. Supplementary Angles • Angles whose sum is 180º 3 and 4 are supplementary.

  7. Theorem • A proven statement of fact

  8. Paragraph Proof/Column Proof • A list of statements and supporting reasons that proves a given statement. ex: If 2x - 7 = 3, then x = 5. 2x – 7 = 3 Given 2x = 10 Addition x = 5 Division

  9. Theorem 2-1Vertical Angles Theorem • Vertical angles are congruent. 1  3 and 2  4

  10. Theorem 2-2Congruent Supplements Theorem • If 2 angles are supplements of the same angle (or of congruent angles), then the 2 angles are congruent. 1 supple 2 3 supple 2 1  3

  11. Theorem 2-3Congruent Complements Theorem • If 2 angles are complements of the same angle (or of congruent angles), then the 2 angles are congruent. 1 comple 2 3 comple 2 1  3

  12. Theorem 2-4 • All right angles are congruent. ABC is a right angle PQR is a right angle ABC  PQR

  13. Theorem 2-5 • If two angles are congruent and supplementary, then each is a right angle. 1  2 1 supple 2 1 is a right angle and 2 is a right angle

  14. Example #1 • Name a. All vertical angles b. Supplementary angles c. Complementary angles d. Adjacent angles

  15. Example #2 • If m3 = 75º, then m1 = _____.

  16. Example #3 • If m4 = 110º, then m3 = _____.

  17. Example #4 • Find the value of x.

  18. Example #5 • What is wrong with this picture?

  19. Example #6 • Find the value of x.

  20. Example #7 • Find the value of x.

  21. Example #8 • Find the value of x and y.

  22. Example #9 • Given: 1 and 2 are vertical angles • Prove: 1  2

  23. Practice 2-5 • #1 - 13 • EXIT

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