# 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