Geometry Study Sheet: Chapter 3 by Tristen Wallace https://padlet.com/20wallacetl/jns0z7bqeh24 Geometry Study Sheet for Ch. 3 which includes all the key terms and 3 example problems en-us 2016-12-14 18:45:43 UTC 2024-06-08 12:50:57 UTC hello@padlet.com parallel lines: coplanar lines that do not intersect 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143695646 2016-12-14 18:47:23 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143695646 skew lines: noncoplanar; they are not parallel and do not intersect 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143695959 2016-12-14 18:48:16 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143695959 parallel planes: planes that do not intersect 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143696116 2016-12-14 18:48:39 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143696116 transversal: a line that intersects 2 or more coplanar lines at distinct points 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143696604 2016-12-14 18:50:02 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143696604 alternate interior angles: nonadjacent interior angles that lie on opposite sides of the transversal 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143696814 2016-12-14 18:50:41 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143696814 corresponding angles: lie on the same side of the transversal (t) and in corresponding positions 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143697026 2016-12-14 18:51:17 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143697026 alternate exterior angles: nonadjacent exterior angles that lie on opposite sides of the transversal 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143697495 2016-12-14 18:52:30 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143697495 Same-Side Interior Angles Postulate (3-1) 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143697786 If a transversal intersects 2 parallel lines, then same-side interior angles are supplementary]]> 2016-12-14 18:53:09 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143697786 Alternate Interior Angles Theorem (3-2) 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143698144 If a transversal intersects 2 parallel lines, then corresponding angles are congruent ]]> 2016-12-14 18:54:05 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143698144 Alternate Exterior Angles Theorem (3-3) 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143699117 If a transversal intersects 2 parallel lines, then alternate interior angles are congruent]]> 2016-12-14 18:57:01 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143699117 Converse of the Corresponding Angles Theorem (3-4) 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143699562 If 2 lines and a transversal form corresponding angles that are congruent, then the lines are parallel]]> 2016-12-14 18:58:14 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143699562 Converse of the Alternate Interior Angles Theorem (3-5) 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143701126 If 2 lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel]]> 2016-12-14 19:03:00 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143701126 Converse of the Same-Side Interior Angles Postulate (3-6) 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143701378 If 2 lines and a transversal form same-side interior angles that are supplementary, then the 2 lines are parallel]]> 2016-12-14 19:03:58 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143701378 Converse of the Alternate Exterior Angles Theorem 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143701549 If 2 lines and a transversal form alternate exterior angles that are congruent, then the 2 lines are parallel]]> 2016-12-14 19:04:29 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143701549 flow proof: arrows show the logical connections between the statements and the reasons are written below the statements 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143701839 2016-12-14 19:05:24 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143701839 Parallel Postulate (3-2) 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143702213 Through a point not on a line, there is one and only one line parallel to the given line]]> 2016-12-14 19:06:47 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143702213 Triangle Angle-Sum Theorem (3-11) 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143702416 The sum of the measures of the angles of a triangle is 180]]> 2016-12-14 19:07:36 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143702416 auxiliary line: a line that you add to a diagram to help explain relationships in proofs 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143702596 2016-12-14 19:08:02 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143702596 exterior angle of a polygon: an angle formed by a side and an extension of an adjacent side 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143702891 2016-12-14 19:08:54 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143702891 remote interior angles: the 2 nonadjacent interior angles of a triangle 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143703076 2016-12-14 19:09:28 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143703076 Perpendicular Postulate (3-3) 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143703376 Through a point not on a line, there is one and only one line perpendicular to the given line ]]> 2016-12-14 19:10:21 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143703376 slope: the slope (m) of a line is the ratio of the vertical change (rise) to the horizontal change (run) between any 2 points 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143703752 2016-12-14 19:11:21 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143703752 slope-intercept form: for a nonvertical line; y = mx + b where m is the slope and b is the y-int 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143704168 2016-12-14 19:12:21 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143704168 point-slope form: 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143705294 2016-12-14 19:15:00 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143705294 Slopes of Parallel Lines 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143705611 -If 2 nonvertical lines are parallel, then their slopes are equal
-If the slopes of 2 distinct nonvertical lines are equal, then the lines are parallel
-Any 2 vertical lines or horizontal lines are parallel]]> 2016-12-14 19:15:59 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143705611 Example Problem #1 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143706425 2016-12-14 19:18:07 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143706425 Example Problem #2 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143706799 2016-12-14 19:19:05 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143706799 Example Problem #3 20wallacetl https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143707566 2016-12-14 19:21:27 UTC https://padlet.com/20wallacetl/jns0z7bqeh24/wish/143707566