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2.6

PROVING STATEMENTS ABOUT ANGLES. 2.6. 1. 2. GOAL. GOAL. Justify statements about congruent angles. Prove properties about special pairs of angles. Properties of special pairs of angles help you determine angles in real-life applications, such as design work. What you should learn.

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2.6

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  1. PROVING STATEMENTS ABOUT ANGLES 2.6 1 2 GOAL GOAL Justify statements about congruent angles. Prove properties about special pairs of angles Properties of special pairs of angles help you determine angles in real-life applications, such as design work. Whatyou should learn Why you should learn it

  2. PROVING STATEMENTS ABOUT ANGLES 2.6 PROPERTIES OF CONGRUENT ANGLES 1 GOAL PROPERTIES OF ANGLE CONGRUENCE Reflexive Symmetric Transitive EXAMPLE 1 VOCABULARY

  3. B Given: Prove: 1 3 2 4 A C EXAMPLE 2 Extra Example 1 StatementsReasons 1. 1. 2. 2. 3. 3. 4. 4. Given Transitive Prop. of  Given Transitive Prop. of 

  4. Given:Prove: 1 2 3 4 Def. of  StatementsReasons 1. 1. Given 2. 2. 3. 3. 4. 4. 5. 5. Extra Example 2 Transitive Prop. of  Given Subs. Prop. of =

  5. EXAMPLE 3 RIGHT ANGLE CONGRUENCE THEOREM All right angles are congruent.

  6. Given: Prove: D C StatementsReasons 1. 1. Given 2. 2. 3. 3. 4. 4. A B Extra Example 3 Transitive Prop. of 

  7. Given: Prove: C B D StatementsReasons 1. 1. Given 2. 2. 3. 3. 4. 4. A F E Transitive Prop. of  Checkpoint

  8. PROVING STATEMENTS ABOUT ANGLES 2.6 2 GOAL USING CONGRUENCE OF ANGLES CONGRUENT SUPPLEMENTS THEOREM CONGRUENT COMPLEMENTS THEOREM EXAMPLE 4 Two angles supplementary to the same angle (or congruent angles) are congruent Two angles complementary to the same angle (or congruent angles) are congruent In proofs, these may be abbreviated as  Supp. Thm. and  Comp. Thm.

  9. Given: Prove: 2 4 3 1 StatementsReasons 1. 1. Given 2. 2. 3. 3. 4. 4. Extra Example 4 Transitive Prop. of =  Complements Thm.

  10. 1. In a diagram, are supplementary and are supplementary. Explain how to show that Using the definition of supplementary angles, So by the transitive property of equality. So by the subtraction property of equality. Therefore, by the definition of congruent angles. LINEAR PAIR POSTULATE EXAMPLE 5 Checkpoint If two angles form a linear pair, then they are supplementary.

  11. In the diagram is right. Explain how to show C B D 2 3 Using the substitution property, you know that by the Angle Addition Postulate. The diagram shows that Substitute 150° for to show 1 4 VERTICAL ANGLES THEOREM A F E EXAMPLE 6 Extra Example 5 Vertical angles are congruent.

  12. Given: are a linear pair,are a linear pair. Prove: 1 2 3 StatementsReasons 1. 1. Given 2. 2. 3. 3. Extra Example 6 Linear Pair Post.  Supplements Thm.

  13. 1. Find the measures of the angles in the diagram given and are complementary and 78° 2 1 3 4 Checkpoint

  14. QUESTIONS?

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