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Undefined Terms

Point) It is a location. It has no size or shape.

Line) Made up of infinite points. At least 2 to form a line. A line has no width or height.

Plane) A plane is a flat surface made up of points. Any 3 points make up a plane. A plane goes in all directions forever.

Distance Formula

Formula) D = √(x₂ - x₁)² + (y₂ - y₁)²

Example) D = √(6 - 2)² + (8 - 5)²

Midpoint Formula

Formula) (x1+x2 /2, y1+y2 /2)

Example) (1+4 /2 , 6+8 /2)

Distance Formula: https://www.calculator.net/distance-calculator.html

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Conditional Statements and Venn Diagrams

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Conditional Statements and Venn Diagrams

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Conditional Statements

This is a statement that can be written in if - then form.

Symbolic form) P -> Q

The hypothesis is the phrase that immediately follows if.

The conclusion is the phrase that immediately follows then.

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

KEY: BOLD: HYPOTHESIS HIGHLIGHT: CONCLUSION.

Venn Diagrams

Types of Venn diagrams:

Circle inside a circle - All elements of _ are elements of _

Touching circles - Some elements of _ are elements of _

Separate circles - There is no relationship between _ and _

Example) Some students who take chorus also take band. This is touching circles.

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Parallel Lines

Parallel lines are 2 coplanar lines that never intersect.

Arrows are used to indicate that lines are parallel.

Example) <-->

<-->

Perpendicular Lines

Meet at 90 degrees.

Negative reciprocal.

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Point-Slope

Formula) Y-Y₁=m(X - X₁)

Example) Y-1=2(X+4)

Standard Form

Ax + By = C

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Triangle Congruence: SSS, SAS, ASA, AAS, HL

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Triangle Congruence: SSS, SAS, ASA, AAS, HL

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SSS) Three pairs of congruent sides

SAS) Two sides and an included angle are congruent.

ASA) Two angles and an included side are congruent.

AAS) Two angles and a side opposite them are congruent.

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

Reasons for congruent sides

Given (you're told)

Definition of midpoint (a midpoint creates two congruent sides)

Reflexive property (a mirror basically. Both sides are the same)

Reasons for congruent angles

Given (you're told)

Vertical angles

Alternate interior angles

Corresponding angles

Definition of angle bisector (a bisector will create 2 congruent angles)

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Definition of a Parallelogram) Quadrilateral in which both pairs of opposite sides are congruent.

Important properties

1. Opposite sides are congruent

2. Opposite angles are congruent

3. Consecutive angles are supplementary (180 degrees)

4. Diagonals bisect each other

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Rectangles have the same properties as parallelograms.

Plus,

1. All four angles = 90 degrees

2. Diagonals are congruent

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Rhombi have the same properties as parallelograms.

Plus,

1. Four sides are congruent

2. Diagonals are perpendicular

3. Diagonals bisect opposite angles

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A square has ALL the properties of a parallelogram, rectangle, and rhombus.

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Non-Isosceles Trapezoids

Properties of Non-Isosceles Trapezoids

1. Only ONE pair of opposite sides are parallel

2. Consecutive angles between parallel lines are supplementary

Isosceles Trapezoids

Isosceles Trapezoids have the same properties as non-isosceles Trapezoids plus these:

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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The midsegment of a trapezoid connects the midpoints of the legs.

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A kite is a quadrilateral with the following properties:

1. Exactly 2 pairs of consecutive congruent sides

2. One pair of opposite angles are congruent

3. Diagonals are perpendicular