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2.7: Substitution and Transitive Property

2.7: Substitution and Transitive Property. The Properties. Substitution – equal quantities may replace each other Transitive – two angles congruent to the same angle are congruent to each other Also works for segments. Example 1. Given: ∠X≅∠Y, ∠X≅∠Z Prove: ∠Y≅∠Z. X. Z. Y. Example 2.

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2.7: Substitution and Transitive Property

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  1. 2.7: Substitution and Transitive Property

  2. The Properties • Substitution – equal quantities may replace each other • Transitive – two angles congruent to the same angle are congruent to each other • Also works for segments

  3. Example 1 • Given: ∠X≅∠Y, ∠X≅∠Z • Prove: ∠Y≅∠Z X Z Y

  4. Example 2 • Given: ∠1≅∠2 • Prove: ∠1 supp. ∠3 2 3 1 M A R K

  5. Example 3 • Given: ∠1 comp. ∠2, ∠3 comp. ∠2 • Prove: ∠1≅∠3 1 2 3

  6. Example 4 • Given: ∠A supp. ∠D, ∠A≅∠C • Prove: ∠C supp. ∠D D C A B

  7. Example 5 • Given: ∠ABD is a right ∠, ∠CBE is a right ∠ • Prove: ∠ABE≅∠CBD C B D A E

  8. Assignment • p. 97 2-6, 15

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