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Lesson 5-R

Lesson 5-R. Chapter 5 Review. Objectives. Review Chapter 5. Vocabulary. None new. Special Segments. Special Segments. M. 51 °. 32°. P. 97 °. N. Sides and Angles. Largest Side is opposite the largest angle Middle Side is opposite the middle angle

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Lesson 5-R

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  1. Lesson 5-R Chapter 5 Review

  2. Objectives • Review Chapter 5

  3. Vocabulary • None new

  4. Special Segments

  5. Special Segments

  6. M 51° 32° P 97° N Sides and Angles • Largest Side is opposite the largest angle • Middle Side is opposite the middle angle • Smallest side is opposite the smallest angle Given: 3 sides or angles measurements 1. Arrange numbers in order requested 2. Replace numbers with side (2 Ltrs) or angle (1 Ltr) 3. Replace with missing letter(s) 97 > 51 > 32 N > M > P MP > NP > MN

  7. Triangle Inequality Theorem • Any two sides must be bigger than the third side • Given three sides (can they make a triangle): Add the smallest two sides togetherIf they are bigger than the largest side, then YesIf they are equal or smaller, then No • Given two sides (find the range of the third side)Min value = Larger number – smaller numberMax value = Larger number + smaller number Min value < third side < Max Value

  8. Triangle Relationship Theorems • SAS Inequality, or Hinge Theorem • SSS Inequality If  ABD <  CBD, then AD < DC A If AD < DC, then  ABD <  CBD D B C This is our virtual alligator problem

  9. Indirect Proof • Step 1: Assume that the conclusion (what we are trying to prove) is false, so then the opposite is true. • Step 2: Show that this assumption leads to a contradiction of the hypothesis, or some other fact, such as a definition, postulate, theorem, corollary or given.Statement Reason part of the proof • Step 3: Point out that because the false conclusion leads to an incorrect statement, the original conclusion must be true (the opposite of what we assumed in step 1)

  10. Summary & Homework • Summary: • 4 special segments of a triangle • Angles correspond to the opposite side in size • Indirect proof: 3 step process • Any 2 sides must be greater than the 3rd • In two triangles that have two congruent sides,the sides opposite the included angles are in the same comparison (bigger or smaller) as the angles • Homework: Study for Ch 5 Test

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