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# Geometry journal 3

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### Geometry journal 3

1. 1. GEOMETRY JOURNAL THREE<br />By: katinarobles<br />
2. 2. Parallel lines & planes<br /> parallel lines: are two lines on the same plane that never touch each other.<br /> AB and CD are parallel<br />parallel planes: planes that never intersect (touch) each other.<br />ADE and SUV are parallel<br />skew lines: two non-parallel lines in different planes that do not intersect. <br />B<br />A<br />D<br />C<br />B<br />D<br />A<br />C<br />S<br />V<br />U<br />A<br />E<br />D<br />
3. 3. Transversal<br /> A transversal is a line that crosses two parallel lines in the same plane.<br />
4. 4. Angles<br /> Corresponding: two pair of angles in the matching corners.<br />Alternate Exterior: two pair of angles on the opposite sides of the transversal but outside the two lines.<br />Alternate Interior: two pair of angles on the opposite sides of the transversal but inside the two line.<br />Same-Side Interior: two pairs of angles on one side of the transversal but inside the two lines.<br />
5. 5. Angles<br /> Corresponding: <1 and <5<br />Alternate Exterior: <2 and <7<br />Alternate Interior: <3 and <6<br />Same-Side Interior: <3 and <5<br />1<br />2<br />3<br />4<br />6<br />5<br />7<br />8<br />
6. 6. Corresponding Angle Postulates<br />If two parallel lines are cut by transversal, then the pairs of corresponding angles are congruent. <br /><1 = <2<br />1<br />2<br />1<br />2<br />2<br />1<br />
7. 7. Corresponding Angle Converse<br /> If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.<br />If <1 = <2, then the lines are parallel.<br />1<br />2<br />1<br />2<br />2<br />1<br />
8. 8. Alternate Interior Angle Theorem<br /> If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent<br /><1 = <2<br />2<br />1<br />1<br />2<br />2<br />1<br />
9. 9. Alternate Interior Angle Converse<br /> If Two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.<br />If <1 = <2, then the lines are parallel.<br />2<br />1<br />1<br />2<br />2<br />1<br />
10. 10. Alternate Exterior Angle Theorem<br /> If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.<br /><1 = <2<br />2<br />1<br />1<br />2<br />1<br />2<br />
11. 11. Alternate Exterior Angle Converse<br /> If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel<br />If <1 = <2, then the lines are parallel.<br />2<br />1<br />1<br />2<br />1<br />2<br />
12. 12. Same-Side Interior Angle Theorem<br /> If two parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary<br /><1 and <2 = 180<br />1<br />2<br />1<br />2<br />2<br />1<br />
13. 13. Same-Side Interior Angle Converse<br /> If two lines are cut by a transversal so that same-side interior angles are supplementary, then the lines are parallel.<br />If <1 and <2 = 180, then the lines are parallel.<br />1<br />2<br />1<br />2<br />2<br />1<br />
14. 14. Perpendicular Transversal Theorem<br /> if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other line also.<br />Interior: <3 = <6, <4 = <5<br />Exterior: <1 = <8, <2 = <7<br />Same-Side: <4 = <6, <3 = <5<br />1<br />2<br />3<br />4<br />6<br />5<br />7<br />8<br />
15. 15. Transitive Property<br />Parallel : If 2 lines are parallel to a third line, then the two lines are parallel to each other.<br />Perpendicular: If 2 lines are perpendicular to a third line, then they are perpendicular to each other<br /> If the transitive line 1, crosses both parallel lines 2&3, then the transitive line 1 is perpendicular to both parallel line 2&3.<br />1<br />2<br />3<br />
16. 16. Slope<br /> Y²-y*1*/x²-x*1*<br />
17. 17. _____(0-10 pts) Describe parallel lines and parallel planes. Include a discussion of skew lines. Give at least 3 examples.<br />_____(0-10 pts) Describe what a transversal is. Give at least 3 examples.<br />_____(0-10 pts) Describe the following angles: Corresponding, alternate exterior, alternate interior and consecutive interior angles. Give an example of each. <br />_____(0-10 pts) Describe the corresponding angles postulate and converse. Give at least 3 examples of each. <br />_____(0-10 pts) Describe the alternate interior angles theorem and converse. Give at least 3 examples of each.<br />_____(0-10 pts) Describe the Same Side interior angles theorem and converse. Give at least 3 examples of each.<br />_____(0-10 pts) Describe the alternate exterior angles theorem and converse. Give at least 3 examples of each.<br />_____(0-10 pts) Describe the perpendicular transversal theorems. Give at least 3 examples. <br />_____(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.<br />
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