angle addition postulate
If B is in the interior of ?AOC, then m?AOB + m?BOC = m?AOC
adjacent angles
Two angles are (blank) if they share a common vertex and side, but have no common interior points
angle
a (blank) consists of two different rays that have the same initial point. The rays are the sides of the (blank) and the initial point is the vertex of the (blank)
subtraction POE
If a=b, then a-c = b-c
obtuse angle
an angle with a measure greater than 90� and less than 180�
congruent segments
two segments are (blank) if they have the same length
segment bisector
a segment, ray, line, or plane that intersects a segment at its midpoint
division POE
If a=b and c?0, then a�0 = b�0
interior of an angle
every nonstriaght angle has an (blank). point D is in the (blank) of ?A if it is between points that lie on each side of the angle
Through any two distinct points...
...there exists exactly one line.
opposite rays
on the line AB, if C is between A and B, then CA-> and CB-> are (blank)
transitive POC
if one geometric object is congruent to a second, and the second is congruent to a third, then the first object is congruent to the third object.
straight angle
an angle with a measure of 180�
acute angle
an angle with a measure greater than 0� and less than 90�
symmetric POC
If one geometric object is congruent to a second, then the second object is congruent to the first.
Through any three non collinear points...
...there exists only one plane.
If two distinct points lie in a plane...
...then the line containing them lies in the plane.
exterior of an angle
Every non straight angle has a (blank). Point D is in the (blank) of ?A if it is not on sides of the angle or in the interior of the angle
multiplication POE
If a=b, then ac=bc
A line is perpendicular to a plane...
...if it is perpendicular to each line in the plane that intersects it.
right angle
an angle with a measure of 90�
reflexive POE
for any real number a, a=a
angle bisector
a ray that divides the angle into two congruent angles
line segment
AB, or (line above) AB, consists of the endpoints A and B and all points on (line with arrows above)AB that lie between A and B
transitive POE
If a=b and b=c, then a=c
midpoint of a segment
the point that divides the segment into two congruent segments
symmetric POE
If a=b, then b=a
addition POE
If a=b, then a+c = b+c
perpendicular lines
two lines are (blank) if they intersect to form a right angle
a line contains...
... at least two points.
reflexive POC
any geometric object is congruent to itself
a plane contains at least...
...three noncollinear points
if two distinct planes intersect...
...then their intersection is a line
collinear
points, segments, or rays that are on the same line
ray
ray AB, or (line with one arrow head to the right) AB, consists of the initial point A and all points on (line with two arrow heads) AB that lie on the same side of A as B lies
segment addition postulate
If B is between A and C, then AB + BC = AC
substitution POE
If a=b, then a may be substituted for b in any equation or expression
congruent angles
two angles are (blank) if they have the same measure
congruent supplements theorem
If two angles are suppl. to the same angle or to congruent angles, then they are congruent
supplementary angles
two angles are (blank) if the sum of their measures is 180�
linear pair postulate
if two angles form a linear pair, then they are suppl.; that is, the sum of their measure is 180�
congruent complements theorem
if two angles are comple. to the same angle or to congruent angles, then they are congruent
vertical angle theorem
if two angles are vertical angles, then they are congruent
vertical angles
two angles are (blank) if their sides form two pairs of opposite rays
complementary angles
two angles are (blank) if the sum of their measures is 90�
linear pair
two adjacent angles are a (blank) if their non common sides are opposite rays
parallel lines
two lines are (blank) if they do not intersect
intersecting lines
are coplaner and have exactly on point in common
oblique lines
lines are (blank) if they intersect and do not form right angles
skew lines
lines are (blank) if they do not lie in the same plane
transitive property of parallel lines
if two lines are parallel to the same line, then they are parallel to each other
property of perpendicular lines
if 2 coplanar lines are perpendicular to the same line, then they are parallel to each other
perpendicular postulate
if there is a line and a point not on a line, them there is exactly one line through the point perpendicular to the given line
parallel postulate
if there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line
If 2 distinct lines intersect...
...then their intersection is exactly one point.
If 2 lines are perpendicular,
then they are intersecting to form 4 right angles
All right angles are
congruent
If 2 lines intersect to form a pair of adjacent congruent angles,
then the 2 lines are perpendicular
tranversal
a line that intersects two or more coplanar lines at different points
corresponding angles
2 angles are (blank) if they occupy the same positions
alternate interior angles
2 angle are (blank) if they lie between line l and m on opposite sides of t
alternate exterior angles
2 angles are (blank) if they lie outside l and m on opposite sides of t
consecutive interior angles
2 angles are (blank) if they lie between l and m on the same side of t
corresponding angles postulate
if 2 lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel
alternate interior angles theorem
if 2 parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent
consecutive interior angles theorem
if 2 parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary
alternate exterior angles theorem
if 2 parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent
perpendicular transversal theorem
if a transversal is perpendicular to one of two parallel lines, then is is perpendicular to the second
congruent triangles
If ?ABC is congruent to ?PQR, then there correspondence between their anglees and sidees such that corresponding angles are congruent and correspoonding sides are congruent
equilateral triangle
a triangle with 3 congruent sides
isosceles triangle
a triangle with at least 2 congruent sides
scalene triangle
a triangle with no congruent sides
acute triangle
a triangle with 3 acute angles
equiangular triangle
a triangle with 3 congruent; each with a measure of 60�
right triangle
a triangle with exactly one right angle
obtuse triangle
a triangle with exactly one obtuse angle
interior of a triangle
the original 3 angles of the triangle
exterior of a triangle
the angles adjacent to the interior angle
Triangle Sum Theorem
The sum of the measure of the interior angles of the trianlge is 180�
Third Angles Theorem
if 2 angles of one triangle are congruent to the 2 angles of a second triangle, then the 3rd angles are congruent
The acute angles of a rigt triangle are
complementary
exterior angle theorem
the measure of an exterior angle of a triangle is equal to the sum of the measures of the 2 nonadjacent interior angles
exterior angle inequality theorem
the measure of an exterior angle of a triangle is greater than the measure of either of the 2 nonadjacent inteior angles
angle addition postulate
If B is in the interior of ?AOC, then m?AOB + m?BOC = m?AOC
adjacent angles
Two angles are (blank) if they share a common vertex and side, but have no common interior points
angle
a (blank) consists of two different rays that have the same initial point. The rays are the sides of the (blank) and the initial point is the vertex of the (blank)
subtraction POE
If a=b, then a-c = b-c
obtuse angle
an angle with a measure greater than 90� and less than 180�
congruent segments
two segments are (blank) if they have the same length
segment bisector
a segment, ray, line, or plane that intersects a segment at its midpoint
division POE
If a=b and c?0, then a�0 = b�0
interior of an angle
every nonstriaght angle has an (blank). point D is in the (blank) of ?A if it is between points that lie on each side of the angle
Through any two distinct points...
...there exists exactly one line.
opposite rays
on the line AB, if C is between A and B, then CA-> and CB-> are (blank)
transitive POC
if one geometric object is congruent to a second, and the second is congruent to a third, then the first object is congruent to the third object.
straight angle
an angle with a measure of 180�
acute angle
an angle with a measure greater than 0� and less than 90�
symmetric POC
If one geometric object is congruent to a second, then the second object is congruent to the first.
Through any three non collinear points...
...there exists only one plane.
If two distinct points lie in a plane...
...then the line containing them lies in the plane.
exterior of an angle
Every non straight angle has a (blank). Point D is in the (blank) of ?A if it is not on sides of the angle or in the interior of the angle
multiplication POE
If a=b, then ac=bc
A line is perpendicular to a plane...
...if it is perpendicular to each line in the plane that intersects it.
right angle
an angle with a measure of 90�
reflexive POE
for any real number a, a=a
angle bisector
a ray that divides the angle into two congruent angles
line segment
AB, or (line above) AB, consists of the endpoints A and B and all points on (line with arrows above)AB that lie between A and B
transitive POE
If a=b and b=c, then a=c
midpoint of a segment
the point that divides the segment into two congruent segments
symmetric POE
If a=b, then b=a
addition POE
If a=b, then a+c = b+c
perpendicular lines
two lines are (blank) if they intersect to form a right angle
a line contains...
... at least two points.
reflexive POC
any geometric object is congruent to itself
a plane contains at least...
...three noncollinear points
if two distinct planes intersect...
...then their intersection is a line
collinear
points, segments, or rays that are on the same line
ray
ray AB, or (line with one arrow head to the right) AB, consists of the initial point A and all points on (line with two arrow heads) AB that lie on the same side of A as B lies
segment addition postulate
If B is between A and C, then AB + BC = AC
substitution POE
If a=b, then a may be substituted for b in any equation or expression
congruent angles
two angles are (blank) if they have the same measure
congruent supplements theorem
If two angles are suppl. to the same angle or to congruent angles, then they are congruent
supplementary angles
two angles are (blank) if the sum of their measures is 180�
linear pair postulate
if two angles form a linear pair, then they are suppl.; that is, the sum of their measure is 180�
congruent complements theorem
if two angles are comple. to the same angle or to congruent angles, then they are congruent
vertical angle theorem
if two angles are vertical angles, then they are congruent
vertical angles
two angles are (blank) if their sides form two pairs of opposite rays
complementary angles
two angles are (blank) if the sum of their measures is 90�
linear pair
two adjacent angles are a (blank) if their non common sides are opposite rays
parallel lines
two lines are (blank) if they do not intersect
intersecting lines
are coplaner and have exactly on point in common
oblique lines
lines are (blank) if they intersect and do not form right angles
skew lines
lines are (blank) if they do not lie in the same plane
transitive property of parallel lines
if two lines are parallel to the same line, then they are parallel to each other
property of perpendicular lines
if 2 coplanar lines are perpendicular to the same line, then they are parallel to each other
perpendicular postulate
if there is a line and a point not on a line, them there is exactly one line through the point perpendicular to the given line
parallel postulate
if there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line
If 2 distinct lines intersect...
...then their intersection is exactly one point.
If 2 lines are perpendicular,
then they are intersecting to form 4 right angles
All right angles are
congruent
If 2 lines intersect to form a pair of adjacent congruent angles,
then the 2 lines are perpendicular
tranversal
a line that intersects two or more coplanar lines at different points
corresponding angles
2 angles are (blank) if they occupy the same positions
alternate interior angles
2 angle are (blank) if they lie between line l and m on opposite sides of t
alternate exterior angles
2 angles are (blank) if they lie outside l and m on opposite sides of t
consecutive interior angles
2 angles are (blank) if they lie between l and m on the same side of t
corresponding angles postulate
if 2 lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel
alternate interior angles theorem
if 2 parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent
consecutive interior angles theorem
if 2 parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary
alternate exterior angles theorem
if 2 parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent
perpendicular transversal theorem
if a transversal is perpendicular to one of two parallel lines, then is is perpendicular to the second
congruent triangles
If ?ABC is congruent to ?PQR, then there correspondence between their anglees and sidees such that corresponding angles are congruent and correspoonding sides are congruent
equilateral triangle
a triangle with 3 congruent sides
isosceles triangle
a triangle with at least 2 congruent sides
scalene triangle
a triangle with no congruent sides
acute triangle
a triangle with 3 acute angles
equiangular triangle
a triangle with 3 congruent; each with a measure of 60�
right triangle
a triangle with exactly one right angle
obtuse triangle
a triangle with exactly one obtuse angle
interior of a triangle
the original 3 angles of the triangle
exterior of a triangle
the angles adjacent to the interior angle
Triangle Sum Theorem
The sum of the measure of the interior angles of the trianlge is 180�
Third Angles Theorem
if 2 angles of one triangle are congruent to the 2 angles of a second triangle, then the 3rd angles are congruent
The acute angles of a rigt triangle are
complementary
exterior angle theorem
the measure of an exterior angle of a triangle is equal to the sum of the measures of the 2 nonadjacent interior angles
exterior angle inequality theorem
the measure of an exterior angle of a triangle is greater than the measure of either of the 2 nonadjacent inteior angles