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Objectives: -Identify and use the Parallel Postulate and the Triangle Sum Theorem

3.5 The Triangle Sum Theorem. Objectives: -Identify and use the Parallel Postulate and the Triangle Sum Theorem. Warm-Up:.

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Objectives: -Identify and use the Parallel Postulate and the Triangle Sum Theorem

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  1. 3.5 The Triangle Sum Theorem Objectives: -Identify and use the Parallel Postulate and the Triangle Sum Theorem Warm-Up: Position one letter in each of the five openings. Do this in such a manner that three numbers are spelled out that total thirteen. Words may be written clockwise and counterclockwise, and individual letters may be shared.

  2. The Parallel Postulate: Given a line and a point not on the line, there is one and only one line that contains the given point and is parallel to the given line.

  3. The Triangle Sum Theorem: The sum of the measures of the angles of a triangle is

  4. Exterior Angle Theorem: The measure of the exterior angles of a triangle are equal to

  5. Example: Two angle measures are given. Find the missing angle measure or state that the triangle does not exist. m<A=, m<C= m<1=, m<3= m<K_, m<M= m<X=, m<Z=

  6. Example: Refer to the diagram below, in which DF||BC, AB||FC, m<ADE=, & m<ACB= m<BDE= A m<DBC= m<CEF= E F D m<AED= m<DEC= B C m<DAE= m<ECF=

  7. Example: Find the indicated angle measure. 3 2 1

  8. Example: Find x and the measure of each angle. x = A m<A= m<B= B C m<C=

  9. Example: Find x and the measure of each angle. x = A m<A= m<B= B C m<C=

  10. Example: Find x and the measure of each angle. x = A m<A= m<B= B C m<C=

  11. Example: Refer to the diagram below to complete the table. 2 3 1 4

  12. 3.5 The Triangle Sum Theorem Cont’d Objectives: -Identify and use Triangle Sum Theorem with algebraic scenarios that require factoring. Warm-Up: Travel through this maze totaling exactly 100 points. No passage or intersection may be used more than once. Enter and exit the maze at the designated arrows.

  13. Factoring / Zero Product Property Review:

  14. Example: Find x and the measure of each angle. m<Y= x = m<W= m<Z= W Y Z

  15. Example: Find x and the measure of each angle. m<B= x = m<A= m<C= A B C

  16. Example: Find x and the measure of each angle. m<E= x = m<D= m<F= D E F

  17. Example: Find x and the measure of each angle. m<B= x = m<A= m<C= A B C

  18. Example: Find x and the measure of each angle. m<E= x = m<D= m<F= D E F

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