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3.1 Lines and Angles

3.1 Lines and Angles. Objective: Students will identify the relationships between 2 lines or 2 planes, and name angles formed by parallel lines and transversals. Definitions. Parallel Lines : coplanar lines that do not intersect Parallel Planes : planes that do not intersect

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3.1 Lines and Angles

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  1. 3.1 Lines and Angles Objective: Students will identify the relationships between 2 lines or 2 planes, and name angles formed by parallel lines and transversals.

  2. Definitions • Parallel Lines: coplanar lines that do not intersect • Parallel Planes: planes that do not intersect • Skew Lines: noncoplanar lines that do not intersect • Transversal: a line that intersects 2 or more lines in a plane at different points

  3. Transversals and Angles 1 2 4 3 5 6 8 7 • Consecutive Interior Angles: <3 & <6, <4 & <5 (also called same side interior angles) • Alternate Exterior Angles: <1 & <7, <2 & <8 • Alternate Interior Angles: <3 & <5, <4 & < 6 • Corresponding Angles: <1 & <5, <2 & <6, <3 & <7, <4 &<8

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  6. 3.2 Properties of Parallel Lines Objective: Students will use the properties of parallel lines to determine congruent angles and angle measures.

  7. Postulates and Theorems • Corresponding Angle Postulate: If 2 || lines are cut by a transversal, then the corresponding <s are congruent. • Alternate Interior Angle Thm: If 2 || lines are cut by a transversal, then alt. int. <s are congruent. • Consecutive Interior Angle Thm: If 2 || lines are cut by a transversal, then cons. Int. <s are suppl. • Alternate Exterior Angle Thm: If 2 || lines are cut by a transversal, then alt. ext. <s are congruent.

  8. Perpendicular Transversal Thm. • In a plane, if a line is perpendicular to one of two || lines, then it is perpendicular to the other.

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