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Proving Segment and Angle Theorems | Understanding Properties | Examples and Exercises

Explore segment and angle theorems, such as reflexive, symmetric, and transitive properties. Learn about congruence, right angle theorems, linear pairs, and solve example problems.

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Proving Segment and Angle Theorems | Understanding Properties | Examples and Exercises

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  1. Warm up (TI) • If m<1 = m<2, then m<2 = m<1. • m<2=m<2. • If EF = GH and GH = IJ then EF = IJ. • If EF = 8 and EF = GH, then GH = 8.

  2. Proving Statements about segments Chapter 2 section 5

  3. Theorem • A theorem is a true statement that follows as a result of other true statements. • A theorem can be proven to be true! Theorem Congruence for segments is reflexive, symmetric and transitive.

  4. That is… • Reflexive: For any segment AB, AB = AB. • Symmetric: If AB = CD, then CD = AB. • Transitive: If AB = CD and CD = EF, then AB = EF. ~ ~ ~ ~ ~ ~

  5. Modified assignment #5 • P. 105 (8-11), p. 107 (28-40)

  6. Proving Statements about Angles 2-6 • Theorem: Angle congruence is also reflexive, symmetric, and transitive. • Based on the previous theorem about segments, can you write examples that illustrate the reflexive, symmetric, and transitive properties?

  7. Right angle congruence theorem • All right angles are congruent. • How do we know this? What leads us to this conclusion? A B

  8. Congruent Supplements Theorem • If two angles are supplementary to the same angle (or to congruent angles) then they are congruent.

  9. Congruent Complements Theorem • If two angles are complementary to the same or to congruent angles, then they are congruent.

  10. Example • Find the measures of the angles in the diagram given <1 and <2 are complementary and <1 = <3 = <4. ~ ~ 78° 2 1 3 4

  11. Linear Pair Postulate • If two angles form a linear pair, then they are supplementary. 2 1 m<1 + m<2 = 180

  12. Vertical Angles Theorem • Vertical angles are congruent! ~ ~ <1 = <3, <2 = <4 1 2 4 3

  13. Example • Solve for each variable 4b +43 8a -3 7a + 8 6b + 17

  14. Modified Assignment #6 • P. 113- 114 (12-17, 27, 28)

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