geometry: chapter 3 Flashcards
skew lines
Nine coplanar lines
parallel lines
Coplanar lines that do not intersect
A line and a plane are parallel if
They do not intersect
parallel planes
planes that do not intersect
theorem 3-1
If two planes are cut by third plane than the lines of intersection are parallel
transversal
A line that intersects to a more coplanar lines in different points
Alternate interior angles
To nonadjacent interior angles on opposite sides of the transversal
postulate 10
If two parallel lines are cut by transversal than corresponding angles are congruent
Same side interior angles
Two adjacent angles on the same side of the transversal
Corresponding angle
Two angles are in corresponding positions relative to the other two lines
theorem 3-2
if two prallel lines are cut by transversal than alternate interior angles are congruent
theorem 3-4
If a transversal was perpendicular to one of two parallel lines that is perpendicular to the other one also
theorem 3-3
If two parallel lines are cut by transversal then same side interior angles are supplementary
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 covered transversal and alternate interior angles are congruent then the lines are parallel
theorem 3-6
If two lines are cut by transversal and the same side into angles are supplementary then the lines are parallel
theorem 3-7
In a plane to 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 give in line
Ways to prove two lines parallel
Show that a pair of corresponding angles are congruent
Show that a pair of alternate interior angles are congruent
show that a pair of same side interior angles are supplementary
In the plane sure that both lines are perpendicular to the third line
theorem 3-10
two lines parallel to a third line are parallel to eachother
triangle
The figure formed by three segments joining three noncollinear points
scalene triangle
no sides congruent
Isosceles triangle
At least two sides congruent
Equilateral triangle
All sides congruent
Acute triangle
Three acute angles
obtuse triangle
One obtuse angle
Right triangle
One right angle
Equiangular triangle
All congruent angles
theorem 3-11
The sum of the measure of the angles of a triangle is 180
corollary 2
each angle of an equal angular triangle has measures 60
corollary 1
If two angles of one triangle are congruent to two angles of another triangle than the third angles are congruent
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
corollary
Something extra
theorem 3-12
The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angle
Polygon
As shape where each segment intersects exactly 2 other segments one at each endpoint and no 2 segments with common endpoint are collinear
convex polygon
No line containing a side of the polygon contains the point in the interior of the polygon
diagonal
A segment joining to nonconsecutive vertices of a polygon
theorem 3-13
This some of the measures of the angle of a convex polygon with n sides is (n-2)180
theorem 3-14
The sum of the measure of the exterior angles of any convex polygon one angle at each vertice is 360
Regular polygon
Both equiangular and equilateral
Inductive reasoning
The conclusion is based on past observation assumed not certain
