Unit 4 Flashcards
Distance Formula
https://www.gstatic.com/education/formulas2/553212783/en/distance_formula.svg
Distance=
Square root
Change in X squared
Plus
Change in Y squared
How to Partition a Line Segment (Formula)
Ratio (X End - X Start) + X Start
Same thing for Y
MUST be in order
Simplifying Radicals
- Find biggest perfect square and divide radical by that
- Simplify perfect square
Midpoint Formula
X 1 plus X 2
Over 2
Comma
Y 1 plus Y 2
Over 2
(X1+X2/2 , Y1+Y2/2)
Slope Intercept form
Y=mx+b
B is the y intercept
X is an X coordinate
Y is a Y coordinate
M is the slope/ rise over run
Point Slope form
Y-Y 1=M(X-X 1)
Variables mean the same thing as slope intercept form
Rules For relationships of lines (parallel and perpendicular)
In order to be parallel, lines must have the same slope
In order to be perpendicular, lines must have opposite reciprocal slopes
Opposite= numerator and denominator are flipped
Reciprocal= opposite sign (ex + becomes - or - becomes +)
Finding missing coordinates
Step 1. Do distance formula
Step 2. Plug in distance and then square both sides of equation
Step 3. Simplify
Step 4. Get ride of squared part on side w k by square rooting
Solve equation with + and - and both are answers
If given enough info you can just count
What is an Altitude
An altitude is drawn perpendicular to the opposite side of a triangle and it creates right triangles
What is a Median
A median is drawn to the midpoint of the opposite side of the a triangle and makes the side it intersects into two = pieces
Formula for Area of a Triangle
A=1/2 bh
Area = one half base times height
Find area of misaligned rectangle
- Count a box around the rectangle
- Calculate the area of whole box
- Calculate total area outside rectangle but inside the box
- Subtract empty spaces area from total drawn box area
Calculating perimeter using distance formula
Use distance formula with given coordinates then multiply by 4 and that’s the answer
Types of Triangles
Scalene: No congruent sides
Isosceles: 2 congruent sides
Equilateral: 3 congruent sides
Acute: If a squared and b squared are greater than c squared (smaller angles)
Right: If a and b squared are = to c squared (Right Angle)
Obtuse: if a and b squared are less than c squared (bigger angles)
Determining types of triangles
Step 1. Do distance formula for all sides to determine if the triangle is scalene, isosceles or equilateral
Step 2. Since I know therefore statement #1
Step 3. Do Pythagorean theorem on distances
4. Do Since I know therefore statement #2
Extra Practice Problems
In unit packets or delta math
How to prove something is a parallelogram
- Do midpoint formula on both diagonals of shape (if they are the same it is a p’gram)
Since: the diagonals have the same midpoint
I know: they bisect each other
Therefore: ABCD is a p’gram
How to prove a rhombus
- Do parallelogram proof
- Do slopes of diagonals
Since: The diagonals have opposite reciprocal slopes
I know: They are perpendicular
Therefore: P’gram ABCD is a rhombus
How to prove a trapezoid
- Do slope on all 4 sides
Since: Only one pair of sides has the same slope
I know: only one pair of sides is parallel
Therefore: ABCD is a trapezoid
How to prove an isosceles trapezoid
- Do trapezoid proof
- Do distance formula on both diagonals
Since: The diagonals have the same distance
I know: They are congruent
Therefore Trapezoid ABCD is isosceles
How to prove a rectangle
- Do parallelogram
- Do distance formulae on both diagonals
Since: The diagonals have the same distance
I know: they are congruent
Therefore: p’gram ABCD is a rectangle
How to prove triangles
- Do distance formula for all sides (all types of triangles)
Since: Triangle ABC has _ side lengths equal (0,2 or 3 side lengths can be equal)
I know: Triangle ABC has _ congruent sides (0, 2 or 3)
Therefore: Triangle ABC is a(n) __ triangle (can be isosceles for 2 sides, scalene for 0 and right for 3)
- Plug in distance values into a squared + b squared = c squared
Since: a squared + b squared __ c squared (can be =, > or <)
I know: Triangle ABC has ___ (can be: “one right angle”, “3 acute angles”, or “one obtuse angle” )
Therefore: Triangle ABC is _ (can be obtuse, acute or right depending on angles)
