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2.7: Substitution and Transitive Property 2.8 Vertical Angles

I can apply the transitive properties of angles & segments . I can apply the substitution property. I can recognize vertical angles. 2.7: Substitution and Transitive Property 2.8 Vertical Angles. Day 1. Substitution. Equal quantities may replace each other. Substitute x = 14 into

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2.7: Substitution and Transitive Property 2.8 Vertical Angles

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  1. I can apply the transitive properties of angles & segments. • I can apply the substitution property. • I can recognize vertical angles. 2.7: Substitution and Transitive Property2.8 Vertical Angles Day 1

  2. Substitution • Equal quantities may replace each other Substitute x = 14 into <A = 2x – 4 If <1 is comp. <2 <2 ≅ <3

  3. Transitive Property • If angles (segments) are congruent to the same angle (segment) or congruent angles (segments), then they are congruent. T O M D A N A C E If TO ≅ OM DA ≅ AN OM ≅AN then If <A ≅ <C <C ≅<E then • Special type of substitution

  4. Opposite Rays • Opposite rays- two collinear rays that have a common endpoint and extend in opposite directions C A A B B but not C

  5. Vertical Angles • Vertical Angles: A pair of non-adjacent angles formed by the intersection of two straight lines • Thm: Vertical angles are congruent ∠1 and ∠3 are vertical angles ∠2 and ∠4 are vertical angles 1 2 4 3

  6. Example 1 • Given: m∠1=37˚ • Find: m∠2, m∠3, m∠4 1 2 4 3

  7. Example 2 • Given: ∠4≅∠6 • Prove: ∠5≅∠6 6 5 4

  8. Example 3 • Given: ∠V≅∠YRX, ∠Y≅∠TRV • Prove: ∠V≅∠Y T V R Y X

  9. Example 4 • Is this possible? (-10x)˚ (-8x-10)˚

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