chapter 3 Flashcards
parallel lines
coplanar lines that do not intersect
skew lines
non coplanar lines (neither parallel nor intersecting)
theorem about parallel planes
If two parallel planes are cut by a third plane, then the lines of intersection are parallel
transversal
a line that intersect two or more coplanar lines in different points
interior angles
inside the two lines cut by the transversal
exteriors angles
outside the two lines cut by the transversal
corresponding angles postulate
If 2 parallel lines are cut by a transversal, then corresponding angles are congruent
Converse:
If 2 lines are cut by a transversal and corresponding angles are congruent, then the two lines are parallel
postulate about alternate interior angles
If 2 parallel lines are cut by a transversal, then alternate interior angles are congruent
converse:
If 2 lines are cut by a transversal and alternate interior angles are congruent, then the two lines are parallel
theorem about same side interior angles
If 2 parallel lines are cut by a transversal, then same-side interior angles are supplementary
converse:
If 2 lines are cut by a transversal and same side interior angles are supplementary, then the two lines are parallel
theorem about perpendicular lines
If a transversal is perpendicular to one of the parallel lines, then it is also perpendicular to the other one.
converse:
If 2 lines are perpendicular to the same line, then the two lines are parallel.
theorems (3)
Through a point outside a line, there is exactly one line parallel to the given line.
Through a point outside a line, there is exactly one line perpendicular to the given line.
Two lines parallel to a third line are parallel to each other.
classification of triangles by sides
equilateral: 3 congruent sides
isosceles: at least 2 congruent sides
scalene: no congruent sides
classification of triangles by angles
acute: 3 acute angles
equiangular: 3 congruent angles (60 degrees)
right: 1 right angle
obtuse: 1 obtuse angle
triangle angle-sum theorem
The sum of the three angles of a triangle is 180
third angle theorem
If 2 angles of one triangle are congruent to 2 angles of another triangle, then the third angles are congruent
angles of equilateral triangles
equilateral triangles are also equiangular, so each angle of an equilateral triangle is 60 degrees.
exterior angle theorem
the measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.
consecutive vertices
2 vertices that are endpoints on the same side
diagonal
a segment that join 2 non consecutive vertices of a polygon
convex polygons
vertices are outside the shape
concave (nonconvex) polygons
at least 1 vertex on the inside
regular polygon
equilateral and equiangular
polygon angle sum formula
n = number of sides
(n-2) x 180
for any polygon (flow)
sum of interior angles: (n-2) x180
sum of exterior angles: 360
for regular polygons (flow)
n (number of sides) = 360/measure of exterior angle
