Geometry journal 3
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This document discusses various geometry concepts related to parallel and perpendicular lines and planes including: parallel lines never intersect and exist on the same plane, parallel planes never touch; skew lines exist in different planes and do not intersect; a transversal is a line that crosses two parallel lines; corresponding, alternate interior/exterior, and same-side interior angles are defined; the corresponding angle, alternate interior angle, and same-side interior angle theorems state relationships between these angles for parallel lines cut by a transversal; and the transitive property applies to parallel and perpendicular lines and their relationships with a third line.
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This document provides information about parallel lines and transversals. It defines key terms like parallel lines, transversals, interior and exterior angles. It describes angle relationships that exist between parallel lines cut by a transversal, such as corresponding angles being congruent, alternate interior angles being congruent, same side interior angles being supplementary. Examples are provided to illustrate these concepts and properties. The document also discusses using these properties to find missing angle measures.
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This document discusses parallel lines and transversals. It defines a transversal as a line that intersects two or more parallel lines at different points. It then explains the four properties of parallel lines cut by a transversal:
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Lines and angles
For those who need help in PPT's for Lines and Angles and want to get good results.
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- 1. GEOMETRY JOURNAL THREE By: katinarobles
- 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.