geometry
Vertex
A point where two or more straight lines meet.
Angle Addition Postulate
for any angle, the measure of the whole is equal to the sum of the measures of its non-overlapping parts
Angle Bisector
a ray that divides an angle into 2 congruent angles
Midpoint
a point that divides a segment into 2 congruent segments
Reflexive Property
A quantity is congruent (equal) to itself. a = a
Symmetric Property
If a = b, then b = a
Transitive Property
If a=b and b=c, then a=c
Complementary Angles
Two angles whose sum is 90 degrees
Supplementary Angles
Two angles whose sum is 180 degrees
Perpendicular
Two lines that intersect to form right angles
Complement Theorem
If the non common sides of two adjacent angles form a right angle,
Supplement Theorem
If two angles form a linear pair, then they are supplementary angles
Congruent Supplements Theorem
If two angles are supplementary to the same angle (or to congruent angles), then they are congruent.
Complements Theorem
Complements of the same angle are equal
Corresponding Angles
Angles in the same place on different lines
Alternate Interior Angles
2 Interior angles that lie on opposite sides of the transversal
Alternate Exterior Angles
Angles that lay outside the parallel lines and are on opposite sides of the transversal; They are congruent.
Consecutive Interior Angles
angles that are on the same side of the transversal and inside the two lines
Transversal
a line that intersects two or more coplanar lines at different points
Converse of the Corresponding Angles
If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel.
Converse of the Alternate Interior Angles
If two coplanar lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the two lines are parallel.
Converse Of Alternate Exterior Angles
If alternate exterior angles are congruent, then the lines are parallel.
Converse Of Consecutive Interior Angles
If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel.
Triangle Angle Sum Theorem
The sum of the measures of the angles of a triangle is 180.
Straight Angle
180 degrees
Congruent Angles
two angles that have the same measure
Adjacent Angles
two angles that share a common vertex and side, but have no common interior points.(corner point)
Vertical Angles
A pair of opposite congruent angles formed by intersecting lines
Linear Pair
a pair of adjacent angles whose non-common sides are opposite rays
Distance Formula
d = √[( x₂ – x₁)² + (y₂ – y₁)²]
Midpoint Formula
(x₁+x₂)/2, (y₁+y₂)/2
Segment Bisector
a line, ray, or segment that divides a segment into two congruent segments
Perpendicular Bisector
A line that is perpendicular to a segment at its midpoint.
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.
Parallel Lines
lines in the same plane that never intersect
Perpendicular Lines
Two lines that intersect to form right angles
Acute Triangle
A triangle that contains 3 angles that are less than 90 degrees.
Obtuse Triangle
A triangle with one angle that is greater than 90 degrees.
Right Triangle
A triangle that has a 90 degree angle.
Equiangular
all angles are congruent having equal angles
Equilateral
having all sides or faces equal
Scalene
A triangle with no equal sides
Isosceles
A triangle that has 2 equal sides.
Isosceles Triangle Theorem
If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent
congruent triangles
2 triangles are congruent if and only if all pairs of corresponding sides and angles are congruent
Congruency Statement
shows which corresponding sides or angles are congruent
CPCTC
An abbreviation for “Corresponding Parts of Congruent Triangles are Congruent,” which can be used as a justification in a proof after two triangles are proven congruent.
SSS
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.(side side side)
SAS
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
ASA
“angle, side, angle” and means that we have two triangles where we know two angles and the included side are equal.
AAS
if two angles and a non-included side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent (angle, angle, side)
HL
Two right triangles are congruent if the hypotenuse and one corresponding leg are equal in both triangles(hypotenuse leg)
Midsegment
segment that connects the midpoints of two sides of a triangle
Triangle Midsegment Theorem
A midsegment of a triangle is parallel to a side of the triangle, and its length is half the length of that side
Angle Bisector Theorem
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle
Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
Median
the middle score in a distribution; half the scores are above it and half are below it
Altitude
the distance between the extended base and the vertex
Parallelogram
A quadrilateral with two pairs of parallel sides
Rhombus
a parallelogram with 4 congruent sides
Rectangle
a parallelogram with 4 right angles
Square
A parallelogram with four congruent sides and four right angles.
Trapezoid
a quadrilateral with only one pair of parallel sides
Isosceles trapezoid
a trapezoid in which the legs are congruent
Kite
A quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.
Ratio
A comparison of two quantities by division
proportion
An equation stating that two ratios are equal
similar figures
Figures that have the same shape but not necessarily the same size
scale factor
The ratio of any two corresponding lengths in two similar geometric figures.
point
A point is an exact position or location on a plane surface
Line
a straight one-dimensional figure having no thickness and extending infinitely in both directions
Line segment
a part of a line that has two
Ray
A part of a line, with one endpoint, that continues without end in one direction
Plane
A flat surface on which a straight line joining any two points that extend forever
Collinear
group of points that lie in the same plane
Non-collinear
points that do not lie on the same line
Coplanar
three or more points which lie in the same plane
Congruent Segments
segments that have the same length
Segment Addition Postulate
If B is between A and C, then AB + BC = AC
Right angle
an angle that measures 90 degrees
Acute angle
an angle that measures Less than 90 degrees
obtuse angle
more than 90 degrees but less than 180 degrees