Ex: 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)

Ex: 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.

  
  

• 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.

  
  

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.

• Ex: If you live in Nashville, then you live in Tennessee.

  Hypothesis: You live in Nashville.

  Conclusion: You live on Tennessee.

  
  

• 2 straight lines that intersect at 90 degrees.

• Symbolic Notation: ⊥

• Perpendicular lines= negative reciprocals.

  Ex. 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

  Ex. 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)

Ex. (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 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

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 ll CD ll EF

• EF= AB+CD/2

  Ex. If AB = 14 and DC = 26, 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)