Geometry chapter 3
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53 terms
Terms | Definitions |
|---|---|
 Parallel Lines | coplanar lines that do not intersect |
| Skew lines | non coplanar lines, therefore, they are neither parallel nor intersecting |
| Parallel planes | do not intersect |
| A line and a plane are parallel | if the do not intersect |
| if two parallel planes are cut by a third plane | then the lines of intersection are parallel (T) |
| transversal | a line that intersects two or more coplanar lines in different points |
| alternate interior angles | two nonadjacent interior angles on opposite sides of the transversal |
| same side interior angles | two interior angles on the same side of the transversal |
| corresponding angles | two angles in corresponding positions relative to the two lines |
| if two parallel lines are cut by a transversal | then corresponding angles are congruent (P) |
| if two parallel lines are cut by a transversal | then alternate interior angles are congruent (T) |
| if two parallel lines are cut by a transversal | then same-side interior angles are supplementary (T) |
| if a transversal is perpendicular to one of two parallel lines | then it is perpendicular to the other one also (T) |
| if two parallel lines are cut by a transversal | then corresponding angles are congruent (P) |
| if two lines are cut by a transversal and corresponding angles are congruent | then the lines are parallel (P) |
| if two lines are cut by a transversal and alternate interior angles are congruent | the the lines are parallel (T) |
| if two lines are cut by a transversal and same-side interior angles are supplementary | then the lines are parallel (T) |
| in a plane two lines perpendicular to the same line | are parallel (T) |
| through a point outside a line | there is exactly one line parallel to the given line (T) |
| through a point outside a line | there is exactly one line perpendicular to the given line (T) |
| two lines parallel to a third line | are parallel to each other (T) |
| triangle | the figure formed by three segments joining three non collinear points |
| scalene triangle | triangle with no sides congruent |
| isosceles triangle | triangle with at least two sides congruent |
| equilateral triangle | triangle with all sides congruent |
| acute triangle | triangle with three acute angles |
| obtuse triangle | triangle with one obtuse angle |
| right triangle | triangle with one right angle |
| equiangular triangle | triangle with all angles congruent |
| auxiliary line | a line (or ray or segment) added to a diagram to help in a proof |
| the sum of the measures of the angles of a triangle | is 180 (T) |
| if two angles of one triangle are congruent to two angles of another triangle | then the third angles are congruent (C) |
| each angle of an equiangular triangle | has measure 60 (C) |
| in a triangle | there can be at most one right angle or obtuse angle (C) |
| the acute angles of a right triangle | are complementary (C) |
| the measure of an exterior angle of a triangle equals | the sum of the measures of the two remote interior angles (T) |
| triangle | three sides |
| quadrilateral | four sides |
| pentagon | five sides |
| hexagon | six sides |
| octagon | eight sides |
| septagon | seven sides |
| nonagon | nine sides |
| decagon | ten sides |
| dodecagon | twelve sides |
| n-gon | n sides |
| diagonal | the segment joining two nonconsecutive vertices |
| the sum of the measures of the angles of a convex polygon with n sides | is (n-2)180 (T) |
| convex polygon | a polygon such that no line containing a side of the polygon contains a point in the interior of the polygon |
| concave polygon | one or more vertex is interior |
| the sum of the measures of the exterior angles of any convex polygon, one angle at each vertex | is 360 (T) |
| regular polygon | if a polygon is both equiangular and equilateral |
| inductive reasoning | a kind of reasoning that is widely used in science and in everyday life |
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