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Undefined: Point, Line, and Plane

Defined: Collinear Points, Coplanar Points, segment, ray, and angle

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1. Opposite sides are parallel

2. Opposite sides are congruent

3. Opposite angles are congruent

4. Consecutive angles are supplementray

5. Diagonals bisect each other

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1. Only one pair of opposite sides are parallel (bases)

2. Consecutive angles are supplementary

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A midsegment of a trapezoid connects the midpoint of the legs. This segment is equal to the average of the two bases

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1. Non-parallel sides (legs) are congruent

2. Diagonals are congruent

3. Base angles are congruent

4. Opposite angles are supplementary

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1. Four congruent sides

2. Diagonals are perpendicular

3. Diagonals bisect opposite angles

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1. Four right angles

2. Diagonals are congruent

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Squares have all the properties of parallelograms, rectangles, and rhombi.

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1. Exactly two pairs of consecutive congruent sides

2. One pair of opposite angles are congruent

3. Diagonals are perpendicular

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1. A location

2. No size or shape

3. Always capital letter

Example: Point A

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1. Made up of infinite points

2. Any 2 points form a line

3. Named by 2 points or lowercase letter

Example: Line AB or Line l

Collinear points- Points that lie on the same line

Non-collinear points- Points that do NOT lie on the same line (must be at least three point)

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1. A flat surface made up of points

2. 3 points make up a plane

3. Extends indefinitely in all directions

4. Named by 3 non-collinear points or uppercase letter

Example: Plane ABC or Plane P

Coplanar points: Points that lie on the same plane

Non-coplanar points: Points that do not lie on the same plane (must be at least four points)

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1. Lines intersect at a point

2. Planes intersect at a line

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1. Formed by 2 rays with a common endpoint

2. endpoint=vertex

3. Named using 3 letters. Middle letter must be vertex.

4. Or named by vertex letter

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1. Acute -90º

2. Obtuse +90º

3. Right 90º

4. Straight 180º

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A angle bisector divides an angle into 2 congruent angles

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A line, segment, or ray perpendicular to a segment at its midpoint

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Two angles across from each other on intersecting lines. They are congruent.

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Two angles next to each other that share a common side

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2 angles whose sum in 90º

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2 angles whose sum is 180º

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2 angles that are adjacent nd supplementary. They form a straight line

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All elements of B are elements of A

p(b)->q(a)

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Some elements of A are elements of B

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There is no relationship between A and B

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Line- 2 coplanar lines that never intersect

Plane- 2 planes that never intersect

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Skew lines that never intersect and are non-coplanar

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A line that intersects two or more lines

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Angles on the same side of the transversal in the same position

Congruent when lines are parallel

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Interior angles, non-adjacent, and on opposite sides of the transversal

Congruent when lines are parallel

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Exterior angles, non-adjacent, and on opposite sides of the transversal

Congruent when lines are parallel

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Interior angles that are on the same side of the transversal

Supplementary (180º) when lines are parallel

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Exterior angles that are on the same side of the transversal

Supplementary when lines are parallel

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Positive- line going up

Negative- line going down

Zero- line going side to side

Undefined- line going up and down

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Graph- rise/run

Ordered Pairs- difference in Y/difference in X

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Parallel- same slope

Perpendicular- negative reciprocals (3/4 to -4/3)

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y-y₁=m(x-x₁)

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y = mx + b

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Ax + By = C

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x=a

a represents x-intercept

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y=a

a represents y-intercept

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Acute- 3 acute angles

Obtuse- 1 obtuse angle

Right- 1 right angle

Equiangular- 3 congruent angles

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Equalateral- 3 congruent sides

Isosceles- 2 congruent sides

Scalene- No congruent sides

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Angle classification, side classification

Ex.- Right, isosceles

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Sum of all 3 angles is 180º

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Angle A + B= D

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A closed figure formed by 3 or more line segments called sides.

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Triangle- Sides: 3 Angle sum: 180

Quadrilateral- Sides 4 Angle sum: 360

Pentagon- Sides: 5 Angle sum: 540

Hexagon- Sides: 6 Angles sum: 720

Heptagon- Sides: 7 Angle sum: 900

Octagon- Sides: 8 Angle sum: 1,080

Nonagon- Sides: 9 Angle sum: 1,260

Decagon- Sides: 10 Angle sum: 1,440

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All sides and angles are congruent

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interior angle sum = (n - 2) x 180°

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The sum of exterior angles of any polygon will equal 360º

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# of sides in a regular polygon when given 1 interior angle

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# of sides in a regular polygon when given 1 interior angle

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Subtract from 180 to get the exterior angle then divide by 360

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Finding the # of sides when we know the angle sum total

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Finding the # of sides when we know the angle sum total

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reverse the interior angles sum formula

divide by 180 then add 2

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3 pairs of congruent sides

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2 sides and an included angle are congruent

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2 angles and an included side are congruent

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2 angles and a side opposite them are congruent

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The hypotenuse and any one leg of a right triangle are congruent

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1. It's Given

2. Definition of a Midpoint (midpoint creates 2 congruent sides)

3. Reflexive Property (A side is congruent to itself)

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1. It's Given

2. Vertical angles

3. Alternate interior angles (parallel lines)

4. Corresponding angles (parallel lines)

5. Definition of Angle Bisector (Bisector creates 2 congruent angles)

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Corresponding Parts of Congruent Triangles are Congruent

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1. A sentence that is either true or false

2. Called Truth Value

3. Represented using letters such as p or q

Ex.- p: supplementary angles have a sum of 180 Truth Value: T

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1. A statement has the opposite truth value

2. shown by symbol ~ (read as not p)

Ex.- ~p: supplementary angles do not have a sum of 180 Truth Value: F

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2 or more statements joined by the words "and" or "or"

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1. Statements joined by the word and

2. written as p^q (conjunction)

3. True when both statements are true

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1. Statements joined by the word or

2. Written as pVq (disjunction)

3. True when at least one statement is true

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1. A statement that can be written if-then form

Smbolic form: p->q (read as if p, then q)

2. The hypothesis is the phrase that immediately follows if

3. The conclusion is the phrase that immediately follows then

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If you live in Nashville, then you live in Tennessee.

Hypothesis: you live in Nashville

Conclusion: you live in Tennessee

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Inverse: formed by negating the hypothesis and conclusion (~p->~q)

Converse: formed by switching the hypotheses and conclusion (q->p)

Contrapositive: formed by negating and switching the hypothesis and conclusion (~q->~p)

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Point A

Line

Plane

Intersecting planes

Angle Bisector

Perpendicular lines

Vertical Angles

Adjacent Angles

Linear Pair

Conditional

Some

No relationship

Transversal

Corresponding angles

Alternate Interior Angles

Alternate Exterior Angles

Consecutive Interior Angles

Consecutive Exterior Angles

Point-Slope to Slope-Intercept

Standard form to Slope-Intercept

Classifying by Angles

Classifying by Sides

Exterior angle theorem

SSS

SAS

ASA

AAS

HL

Parallelograms

Trapezoids

Midsegment of a trapezoid

Isosceles Trapezoids

Rhombus

Rectangle

Square

Kite

Distance Formula

Midpoint Formula

Point-Slope Form

Slope-Intercept Form

Standard Form

Interior Angle Sum Formula

Interior angle of a regular polygon