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Geometry

Geometry. Agenda 1. ENTRANCE 2. go over Practice 1-6 3. 2-5 Proving Angles Congruent 4. Practice Assignment 5. EXIT. Chapter 1. 2-5 Proving Angles Congruent. Vertical Angles. Opposite angles formed by intersecting lines The opposite angles are _______ and _______.

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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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