Geometry Study Sheet: Chapter 5 by Tristen Wallace https://padlet.com/20wallacetl/al9y5rkwsbsy All of chapter 5 key terms along with 3 example problems en-us 2016-12-18 20:47:38 UTC 2023-05-11 08:05:24 UTC hello@padlet.com mid segment of a triangle: a segment connecting the midpoints of two sides of the triangle 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144242085 2016-12-18 20:52:39 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144242085 Triangle Midsegment Theorem (5-1) 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144242154 If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and is half as long]]> 2016-12-18 20:54:02 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144242154 equidistant: if a point is the same distance from two objects 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144242738 2016-12-18 21:04:21 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144242738 Perpendicular Bisector Theorem (5-2) 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144242775 If a point is on the perpendicular bisector of a segment, the it is equidistant from the endpoints of the segment]]> 2016-12-18 21:05:11 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144242775 Converse of the Perpendicular Bisector Theorem (5-3) 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144242822 If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment]]> 2016-12-18 21:06:00 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144242822 distance from a point to a line: the length of the perpendicular segment from the point to the line 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144242850 2016-12-18 21:06:45 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144242850 Angle Bisector Theorem (5-4) 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144242878 If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle]]> 2016-12-18 21:07:16 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144242878 Converse of the Angle Bisector Theorem (5-5) 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144242914 If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector]]> 2016-12-18 21:07:50 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144242914 concurrent: when 3 or more lines intersect at one point 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243011 2016-12-18 21:09:57 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243011 point of concurrency: the point in which 3 or more (concurrent) lines intersect 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243025 2016-12-18 21:10:10 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243025 Concurrency of Perpendicular Bisectors Theorem (5-6) 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243058 The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices]]> 2016-12-18 21:10:52 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243058 circumcenter of the triangle: the point of concurrency of the PERPENDICULAR BISECTORS of a triangle 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243116 2016-12-18 21:12:14 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243116 circumscribed about: when one draws a circle around the triangle 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243129 2016-12-18 21:12:24 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243129 where is the circumcenter located? 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243154 it can be inside an acute triangle, on a right triangle, and outside an obtuse triangle]]> 2016-12-18 21:12:56 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243154 Concurrency of Angle Bisectors Theorem (5-7) 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243221 The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides of the triangle]]> 2016-12-18 21:14:18 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243221 incenter of the triangle: the point of concurrency of the angle bisectors of a triangle 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243255 2016-12-18 21:15:01 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243255 inscribed in: when a circle is drawn inside of a triangle 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243276 2016-12-18 21:15:22 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243276 indirect reasoning: all possibilities are considered and then all but one are proved false so the remaining possibility must be true 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243309 2016-12-18 21:16:09 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243309 indirect proof: a proof involving indirect reasoning 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243336 2016-12-18 21:16:51 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243336 Comparison Property of Inequality 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243403 If a = b + c and c > 0, then a > b]]> 2016-12-18 21:18:02 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243403 Corollary to the Triangle Exterior Angle Theorem (5-9) 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243446 The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles]]> 2016-12-18 21:18:49 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243446 Theorem 5-10 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243500 If 2 sides of a triangle are not congruent, then the larger angle lies opposite the longer side]]> 2016-12-18 21:19:51 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243500 Theorem 5-11 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243622 If 2 angles of a triangle are not congruent, then the longer side lies opposite the larger angle ]]> 2016-12-18 21:22:03 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243622 Triangle Inequality Theorem 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243682 The sum of the lengths of any two sides of a triangle is greater than the length of the third side]]> 2016-12-18 21:23:09 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243682 SAS Theorem (5-13) 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243740 If 2 sides of one triangle are congruent to two sides of another triangle, and the included angles are not congruent, then the longer third side is opposite the larger included angle]]> 2016-12-18 21:24:11 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243740 SSS Theorem (5-14) 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243873 If 2 sides of one triangle are congruent to two sides of another triangle, and the third sides are not congruent, then the larger included angle is opposite the longer third side]]> 2016-12-18 21:27:51 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144243873 Example #3 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144246221 2016-12-18 22:25:27 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144246221 Example #2 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144246226 2016-12-18 22:25:33 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144246226 Example #1 20wallacetl https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144246230 2016-12-18 22:25:54 UTC https://padlet.com/20wallacetl/al9y5rkwsbsy/wish/144246230