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Understanding Proofs Involving Parallel Lines and Angle Relationships in Geometry

This unit focuses on the critical concepts and proofs associated with parallel lines and their angle relationships in geometry. It covers essential definitions such as corresponding angles, alternate interior angles, and supplementary angles, along with their properties and theorems. The material emphasizes establishing congruence and supplementary relationships through proofs, utilizing key postulates and logical reasoning. By exploring various line and angle relationships, learners will enhance their ability to navigate geometrical proofs effectively.

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Understanding Proofs Involving Parallel Lines and Angle Relationships in Geometry

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  1. Geometry Unit II 3.3 Part 2 Proofs Involving Parallel Lines

  2. given postulate Theorem definition Linear pairs A ray that divides an angle into congruent angles add up to 180 degrees

  3. Two parallel lines The pairs of CORRSP. angles are congruent = 180 degrees Replacing one quantity with an equivalent one. They are congruent AIA are congruent AEA are congruent SSIA are supplementary.

  4. a II c, b II d Given 2. Are corresponding angle Def. of corrs. Angles _______ CAP 4. _____ Def alt. ext angles Alternative Exterior Angles 5. ________ AEAT 6. _________ Substitution

  5. 1. a II c, b II d Given 2. Are same side interior angles Def. same side INT Angle 3. Are supplementary SSIAT 4. Def. of supplementary angles 5. Are Alt. ext. angles Def. of Alt. Ext. Angles 6. AEAT 7. Substitution 8. Are supplementary Def. of supplementary

  6. A E B 1. BE II LD, BE bisects angle ABD Given 2. Def of Ang. Bisector L 3. Are Alt. Int. Angle Def. Alt. Int D 4. AIAT 5. Substitution

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