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A) Foundation of Geometry (undefined terms, distance formula, midpoint formula)

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A) Foundation of Geometry (undefined terms, distance formula, midpoint formula)

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Distance formula: D=√(x2-x1)2+(y2-y1)2

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.

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B) Conditional Statements and Venn Diagrams

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B) Conditional Statements and Venn Diagrams

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Venn Diagram: Venn diagrams are a useful way to show relationships.

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.

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Perpendicular lines:

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

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Point- Slope Form- When given a point (x1, y1) through which the line passes and the slope of the line (m), we can write the equation in point-slope form.

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.

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

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

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SSS- Three pairs of congruent sides.

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.

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Parallelogram- A quadrilateral in which both pairs of opposite sides are parallel.

Properties:

Opposite sides are congruent.

Opposite angles are congruent.

Consecutive angles are supplementary.

Diagonals bisect each other.

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Opposite sides are congruent.

Opposite sides are parallel.

Opposite angles are congruent.

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Opposite sides 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.

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Opposite angles are congruent.

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.

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Isosceles trapezoids

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.

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Midsegment of a Trapezoid

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

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Kite

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)

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A) 1. https://www.youtube.com/watch?v=iSith91Dm_M

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