Example: Find EF given E(-7,-2) and F(11,3).

d=√(11-(-7))2+(3-(-2))2

d=√349

d=√18.6815

Midpoint formula: (x1+x2/2,y1+y2/2)

Example: Find the midpoint of line GH given G(7,-5) and H(9,-1).

(7+9/2,-5+-1/2)=(8,-3)

Undefined terms:

Point- a point is a location.

Line- a line is made of infinite points.

Plane- a plane is a flat surface made up of any three points.

Types of Venn Diagrams:

All elements of p are elements of q.

Some elements of p are elements of q.

There is no relationship between p and q.

Conditional Statements

A statement that can be written in If-Then form.

The hypothesis immediately follows if.

The conclusion immediately follows then.

Types of conditional statements:

-Inverse- negating the hypothesis and conclusion.

-Converse- switching the hypothesis and conclusion.

-Contrapositive- negating and switching the hypothesis and conclusion.

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

Hypothesis: You live in Nashville.

Conclusion: You live in Tennessee.

2 straight lines that intersect at 90 degrees.

Symbolic Notation: ⊥

Perpendicular lines= negative reciprocals.

Example: A(0,2), B(5,4), C(1,8), D(3,3)

4-2/5-0=2/5 3-8/3-1=-5/2 = perpendicular

Parallel lines:

2 coplanar lines that never intersect.

arrowheads are used to indicate the lines are parallel.

Symbolic Notation: ∥

Parallel lines= same slope

Example: A(-3, 13), B(4, -15), C(-2,5), D(1,-7) -15-13/4-(-3)=-28/7=-4-7-5/1-(-2)=-12/3=-4

=parallel

Point-Slope Form: y-y1=m(x-x1)

Example: (4,1): slope=2

y=1=2(x-4)+1

y=2x-8+1

y=2x-7

Standard Form: Ax+ By= C

Because standard form does not give you slope (m) you must be able to convert them to slope intercept form.

SAS- Two sides and an included angle.

ASA- Two angles and an included side.

AAS- Two angles and a none included side.

HL- The hypotenuse and any one leg of a right angle.

Properties:

Opposite sides are congruent.

Opposite angles are congruent.

Consecutive angles are supplementary.

Diagonals bisect each other.

Opposite sides are parallel.

Opposite angles are congruent.

Opposite sides are parallel.

Opposite angles are congruent.

All sides are congruent.

Consecutive angles are supplementary.

Diagonals bisect each other.

Diagonals are perpendicular.

Diagonals bisect opposite angles.

Opposite sides are parallel

Opposite angles are congruent.

Consecutive angles are supplementary.

Diagonals bisect each other.

Four right angles.

Diagonals are congruent.

Four congruent sides.

Diagonals are perpendicular.

Diagonals bisect opposite angles.

Properties:

Non-parallel sides (legs) are congruent.

Diagonals are congruent.

Base angles are congruent.

Opposite angles are supplementary.

Non-isosceles trapezoids

Properties:

Only ONE pair of opposite sides are parallel.

Consecutive angles between parallel lines are supplementary.

The midsegment of a trapezoid connects the midpoint of the legs: If EF is the midsegment of trapezoid ABCD, then:

AB ∥ CD ∥ EF

EF= AB+CD/2

Example: If AB = 14 and DC = 25,

find EF

44+26=40/2=20

EF=20

A kite is a quadrilateral with the following properties:

Exactly two pairs of consecutive congruent sides. (AB=AD and BC=DC)

One pair of opposite angles are congruent. (angle ABC = to angle ADC)

Diagonals are perpendicular. (AC is perpendicular to BD)

2. https://science.howstuffworks.com/math-concepts/distance-formula.htm

3. https://study.com/learn/lesson/what-is-the-midpoint-formula.html

B) https://slideplayer.com/slide/9750849/

C) https://sciencenotes.org/parallel-and-perpendicular-lines/

D) 1. https://study.com/academy/lesson/standard-form-equations-formulas-quiz.html

2. https://www.youtube.com/watch?v=yoHs1h5qtuQ

E) https://knowunity.com/knows/geometry-triangle-proofs-sss-sas-1a2080b0-3f97-4351-9150-4ff95f7a3ec0

F) https://www.cuemath.com/geometry/parallelograms/

G) https://www.youtube.com/watch?v=Ov4aTty67A8

H) https://www.youtube.com/watch?v=uXo_Vpctmrg

I) https://calcworkshop.com/quadrilaterals/special-parallelograms/

J) 1. https://www.youtube.com/watch?v=AlyWS8bG3kE

2. https://mathmonks.com/trapezoid/non-isosceles-or-scalene-trapezoid

K) https://andymath.com/trapezoid-midsegment/

L) https://www.youtube.com/watch?v=UTgF6lSAMa8