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2.6 Proving Angles Congruent

2.6 Proving Angles Congruent. Definitions. Given: Information that is provided up front You do not have to make any conclusions or apply any theorems to use it Prove: Facts that you are requested to prove using the information that is given and previously learned theorems and postulates.

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2.6 Proving Angles Congruent

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  1. 2.6 Proving Angles Congruent

  2. Definitions • Given: • Information that is provided up front • You do not have to make any conclusions or apply any theorems to use it • Prove: • Facts that you are requested to prove using the information that is given and previously learned theorems and postulates

  3. Theorem • A true statement that follows as a result of other true statements. • All theorems MUST be proven! • Postulates and axioms are used to prove theorems

  4. 2-Column Proof • Numbered statements and corresponding reasons in a logical order organized into 2 columns. statements reasons 1. 1. 2. 2. 3. 3. etc

  5. Right Angle Theorem (2.3) • All Right Angles are Congruent

  6. Congruent Supplements Theorem (2.4) • If two angles are supplementary to the same angle (or to congruent angles) then they are congruent • If m<1 + m<2 = 180o and m<2 + m<3 = 180o, then <1 <3 2 1 3

  7. Congruent Complements Theorem (2.5) • If two angles are complementary to the same angle (or to congruent angles) then the two angles are congruent • If m<4 + m<5 = 90o, and m<5 + m<6 = 90o, then <4 <6 5 6 4

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

  9. Vertical Angles Theorem (2.6) • Vertical Angles are congruent • <1 <3; <2 <4 2 1 3 4

  10. Using the Vertical Angles Theorem • What is the value of x?

  11. Homework • Classwork – p. 124 – 127 #6 – 12, 16, 17, 20 – 22, 26 – 29, 33 – 35 ALL. • Homework – 6-7, 12, 16, 20-22 even, 26-29, 34

  12. Paragraph Proofs • A paragraph proof is another way a proof is often written • The advantage of a paragraph proof is that you have the chance to explain your reasoning in your own words • In a paragraph proof, the statements and their justifications are written together in a logical order in a paragraph form.

  13. Predictions • a. What information does the first sentence of a paragraph proof contain? • b. What information does the last sentence of a paragraph proof contain?

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