Geometry 1-1 to 2-6
opposite ray
the opposite direction of a ray
theorem 1-2
through a line and a point not in the line there is exactly one plane
supplementary angles
2 angles whose measures have the sum of 180
reflexive property
AB is congruent to AB or M1 is congruent to M1
bisector of a segment
a line, ray, segment, or plane that intersects a segment at its midpoint
congruent angles
angles with equal measure
angle
formed by two rays with a common endpoint called the vertex of the angle. The two rays are sides of the angle
point
gives locations
postulate 8
if 2 points are in a plane, then the line that contains the points is in that plane
postulate 9
if 3 planes intersect, then their intersection is a line
transitive property
if A=B and B=C, then A=C
symmetric property
if A=B, then B=A
division property
if AB=CD, then 1/2AB=1/2CD
multiplication property
if AB=CD, then 2AB=2CD
segment addition postulate
if B is between A&C, then AB+BC=AC AC=AB+BC AC=2+12 AC=14
substitution property
if a=b,then either a or b can be substituted for the other in any equation or inequality
theorem 2-6
if the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary
theorem 2-8
if two angles are complements of congruent angles (or the same angle), then the two angles are congruent **no substitution** comps of congruent angles are congruent comps of the same angle are congruent
theorem 2-7
if two angles are supplements of congruent angles (or the same angle), then the two angles are congruent **no substitution** supplements of congruent angles are congruent supplements of the same angles are congruent
theorem 2-4
if two lines are perpendicular, then they form congruent adjacent angles
theorem 2-5
if two lines form congruent, adjacent angles, then the lines are perpendicular
theorem 1-3
if two lines intersect, then exactly one plane contains the lines
theorem 1-1
if two lines intersect, then they intersect in exactly one point
acute angle
measure between 0 and 90
segment
on endpoints
coplanar points
points all in one plane
collinear points
points all on one line
intersection
points in common (pt d is the intersection for a,b,c and e
congruent segments
segments that have equal length
space
set of all points
additional property
if M1=M2, then M1+M3=M2+M3
subtraction property
if M1=M2, then M1-M3=M2-M3
angle bisector theorem
if OB is a bisector of angle AOC, then measurement angle AOB= 1/2 measurement angle AOC measurement angle BOC= 1/2 measurement angle AOC
obtuse angle
measure between 90 and 180
postulate 7
through any 3 points, there is at least one plane and through any 3 non-collinear points there os exactly one plane
postulate 6
through any two points there is exactly one line
plane
two dimensions that has length+width and line that goes forever
perpendicular lines
two lines that intersect to form right angles (if L is perpendicular to M, then the measure of angle 1 becomes 90 degrees, then L is perpendicular to M)
postulate 5
- a line contains at least 2 points - a plane contains at least 3 points, not all on one line - space contains at least 4 points, not all in one plane
complementary angles
2 angles whose measures have the sum of 90
straight angle
=180
right angle
=90
bisector of an angle
a ray which divides an angle into 2 congruent adjacent angles
adjacent angles
angles with common vertex and a common side, but no common interior points
line
has dimensions
congruent
having the same size and shape
midpoint of a segment
if B is the midpoint of AC, then AB is congruent to BC
angle addition postulate
if B lies in the interior of angle AOC, then measurement angle AOB+measurement angle BOC= measurement angle AOC
theorem 2-1
if M is the midpoint of AB, then AM= 1/2AB+BM1/2AB
ray
the point on the left side is the end point and the point on the right side goes forever