Unit 3: Parallel Lines & Planes Flashcards
parallel lines
coplanar lines that do not intersect
skew lines
noncoplanar lines that are neither parallel nor intersecting
parallel planes
planes that do not intersect
when are a line and a plane parallel?
when they don’t intersect
a plane intersecting 2 parallel planes
if 2 parallel planes are cut by a third plane, then the lines of intersection are parallel
transversal
a line that intersects 2+ coplanar lines in different points
alternate interior angles
2 nonadjacent interior angles on opposite sides of the transversal
same side interior angles
2 interior angles on the same side of the transversal
corresponding angles
2 angles in corresponding positions relative to the 2 lines
corresponding angles postulate
if 2 lines are cut by a transversal, then the corresponding angles are congruent
alternate interior angles theorem
if 2 parallel lines are cut by a transversal, then the alternate interior angles are congruent
same side interior angles theorem
if 2 parallel lines are cut by a transversal, then the same side interior angles are supplementary
perpendicular transversal theorem
if a transversal is perpendicular to 1 of 2 parallel lines, then it is also perpendicular to the other line as well
corresponding angles theorem converse
if a transversal cuts 2 lines such that the corresponding angles are congruent, then the 2 lines are parallel
alternate interior angles theorem converse
if 2 lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel
same side interior angles theorem converse
if 2 lines are cut by a transversal and the same side interior angles are supplementary angles, then the lines are parallel
perpendicular transversal theorem converse
in a plane, 2 lines perpendicular to the same line are also parallel
parallel postulate
through a point outside a line, there is exactly 1 line parallel to the given line
perpendicular postulate
through a point outside a line, there is exactly 1 line perpendicular to the given line
parallel lines transitivity theorem
2 lines parallel to a third line are parallel to each other
triangle sum theorem
the sum of the measures of a triangle ins 180
triangle sum corollaries
- if 2 angles of 1 triangle are congruent to two angles of another triangle, the three angles are congruent
- each angle of an equiangular triangle is 60
- in a triangle, there is at most one right or obtuse angle
- the acute angles of a right triangle are complementary
exterior angles theorem
the measure of the exterior angle of a triangle is the sum of the measure of 2 of its remote interior angles
acute, obtuse, right, and equiangular
a triangle with….
acute: 3 acute angles
obtuse: 1 obtuse angle
right: 1 right angle
equiangular: all (3) congruent angles
scalene, isosceles, equilateral
a triangle with…
scalene: no congruent sides
isosceles: at least 2 congruent sides
equilateral: all (3) congruent sides
polygon
a shape where…
1. each segment intersects with exactly 2 others at 1 endpoint
2. no 2 segments sharing 1 endpoint are collinear
convex polygon
a polygon with no sides pointing into its interior
diagonal
a segment joining two nonconsecutive vertices
polygon interior sum theorem
the sum of a convex polygon’s interior angles w/ n sides is (n-2)180
polygon exterior sum theorem
the sum of the measures of a convex polygon’s exterior angles w/ n sides is 360
concave polygons
when 1+ diagonal crosses outside the polygon
irregular polygons
a polygon that is neither equiangular nor equilateral, much less regular
