2. Parallel lines & planes parallel lines: are two lines on the same plane that never touch each other. AB and CD are parallel parallel planes: planes that never intersect (touch) each other. ADE and SUV are parallel skew lines: two non-parallel lines in different planes that do not intersect. B A D C B D A C S V U A E D
3. Transversal A transversal is a line that crosses two parallel lines in the same plane.
4. Angles Corresponding: two pair of angles in the matching corners. Alternate Exterior: two pair of angles on the opposite sides of the transversal but outside the two lines. Alternate Interior: two pair of angles on the opposite sides of the transversal but inside the two line. Same-Side Interior: two pairs of angles on one side of the transversal but inside the two lines.
5. Angles Corresponding: <1 and <5 Alternate Exterior: <2 and <7 Alternate Interior: <3 and <6 Same-Side Interior: <3 and <5 1 2 3 4 6 5 7 8
6. Corresponding Angle Postulates If two parallel lines are cut by transversal, then the pairs of corresponding angles are congruent. <1 = <2 1 2 1 2 2 1
7. Corresponding Angle Converse If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. If <1 = <2, then the lines are parallel. 1 2 1 2 2 1
8. Alternate Interior Angle Theorem If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent <1 = <2 2 1 1 2 2 1
9. Alternate Interior Angle Converse If Two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel. If <1 = <2, then the lines are parallel. 2 1 1 2 2 1
10. Alternate Exterior Angle Theorem If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. <1 = <2 2 1 1 2 1 2
11. Alternate Exterior Angle Converse If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel If <1 = <2, then the lines are parallel. 2 1 1 2 1 2
12. Same-Side Interior Angle Theorem If two parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary <1 and <2 = 180 1 2 1 2 2 1
13. Same-Side Interior Angle Converse If two lines are cut by a transversal so that same-side interior angles are supplementary, then the lines are parallel. If <1 and <2 = 180, then the lines are parallel. 1 2 1 2 2 1
14. Perpendicular Transversal Theorem if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other line also. Interior: <3 = <6, <4 = <5 Exterior: <1 = <8, <2 = <7 Same-Side: <4 = <6, <3 = <5 1 2 3 4 6 5 7 8
15. Transitive Property Parallel : If 2 lines are parallel to a third line, then the two lines are parallel to each other. Perpendicular: If 2 lines are perpendicular to a third line, then they are perpendicular to each other If the transitive line 1, crosses both parallel lines 2&3, then the transitive line 1 is perpendicular to both parallel line 2&3. 1 2 3
17. _____(0-10 pts) Describe parallel lines and parallel planes. Include a discussion of skew lines. Give at least 3 examples. _____(0-10 pts) Describe what a transversal is. Give at least 3 examples. _____(0-10 pts) Describe the following angles: Corresponding, alternate exterior, alternate interior and consecutive interior angles. Give an example of each. _____(0-10 pts) Describe the corresponding angles postulate and converse. Give at least 3 examples of each. _____(0-10 pts) Describe the alternate interior angles theorem and converse. Give at least 3 examples of each. _____(0-10 pts) Describe the Same Side interior angles theorem and converse. Give at least 3 examples of each. _____(0-10 pts) Describe the alternate exterior angles theorem and converse. Give at least 3 examples of each. _____(0-10 pts) Describe the perpendicular transversal theorems. Give at least 3 examples. _____(0-10 pts) Describe how the transitive property also applies to parallel and perpendicular lines. Include a discussion about the perpendicular line theorems. Give at least 2 examples of each.
