Chapter 3 Flashcards
parallel lines
coplanar lines that do not intersect
skew lines
non coplanar lines that are not parallel nor intersecting
parallel planes
planes that do not intersect
theorem 3-1
if 2 parallel lines are cut by a third plane, then the lines of intersection are parallel
transversal
line that intersects two or more coplanar lines in unique 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
theorem 3-2
if two parallel lines are cut by a transversal, then alternate interior angles are congruent
theorem 3-3
if two parallel lines are cut by a transversal, then same-side interior angles are supplementary
theorem 3-4
if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also
postulate 11
if two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel
theorem 3-5
if two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel
theorem 3-6
if two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel
theorem 3-7
in a plane two lines perpendicular to the same line are parallel
theorem 3-8
through a point outside a line, there is exactly one line parallel to the given line
theorem 3-9
through a point outside a line, there is exactly one line perpendicular to the given line
theorem 3-10
two lines parallel to a third line are parallel to each other
scalene triangle
no sides congruent
isosceles triangle
at least two sides congruent
equilateral triangle
all sides congruent
acute
three acute angles
obtuse
one obtuse angle
right
one right angle
equiangular
all angles congruent
theorem 3-11
the sum of the measures of the angles of a triangle is 180
third angles theorem
if 2 angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent
corollary 2
each angle of an equiangular triangle measure 60
corollary 3
in a triangle, there can be at most one right angle or obtuse angle
corollary 4
the acute angles of a right triangle are complementary
theorem 3-12
the measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles
polygon
many angles
convex polygon
a polygon such that no line containing a side of the polygon contains a point in the interior of the polygon
diagonal
segment joining two nonconsecutive vertices
theorem 3-13
the sum of the measures of the angles of a convex polygon with n sides is (n-2)180
theorem 3-14
the sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 360
inductive reasoning
- conclusion based on several past observations
- conclusion is probably true, but not necessarily true
