Chapter 2 Ultimate Study Deck Flashcards
Speed run Life baby
What is the Pythagorean Theorem?
a² + b² = c²
Distance Formula (1)
(For a horizontal or vertical line)
|B - A|
How do you find the distance of a diagonal line
- Label points
- Find length of base & height ( a & b )
- Use Pythagorean Theorem
What is zero slope?
When there is no change in the y coordinates
0/1
What is vertical/undefined slope?
when there is no change in the x coordinates
1/0
How to find slope?
Slope Formula: yB - yA/xB - xA
Basically:
Vertical Change (Change in y)/Horizontal Change (Change in x)
What is the Midpoint Formula?
M = (x1 + x2)/2 , (y1 + y2)/2
Used when given two points and asked the midpoint
Distance Formula (2)
(Used with Diagonal Lines)
√(x2 - x1)² + (y2 - y1)²
How do you prove that two lines are parallel?
Using the slope formula prove that both lines have the same slope.
What is the Inverse Property of Addition?
Adding a number and its opposite additive inverse will produce the sum of zero
Algebraic Proofs with Parallel Lines
Lines that are parallel have no common points, therefore, if you try to solve for “x” there should be no solution.
Slopes of Perpendicular lines have…
opposite reciprocal slopes.
- Change the signs
- Flip the fraction
What is literally the best way to find a slope???
y = mx + b
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What are Tranversals
A line that intersects two or more lines on the same plane.
What is the Corresponding Angles Theorem?
If two parallel lines are cut in half by a transversal line than the corresponding lines are congruent
What is the Alternate Interior Lines Theorem?
If two parallel lines are cut in half by a transversal than the alternate interior lines are congruent
What is the Alternate Exterior Lines Theorem?
If two parallel lines are cut in half by a transversal line than alternate exterior angles are congruent.
What is the Same Side Angles theorem?
If two parallel lines are cut by a transversal than the pairs of same side interior angles are supplementary.
(Equal 180)
What is the Perpendicular Bisector Theorem?
If a point lies on the perpendicular bisector of a line segment, the the point is equidistant from the other endpoints of the segment.
What is the ratio for midpoints?
1:1 (Line divided into two)
What is the Line Ratio Equation?
C = A + ᵃ⁄a+b(B - A)
How do you find a random point with a ratio on a slanted line?
Xc = XA + ᵃ⁄a+b(XB - XA)
Yc = YA + ᵃ⁄a+b(YB - YA)
(Can also be used when trying to figure out equally spread out points across a slanted line with a given A and B)
When trying to find “B” on a slanted line with a given “A” and “C” then-
- take notice of ratio and use Xc = axB +bxA/(a+b)
You can also use Yc = ayB + byA/(a+b)
How do you find the Area of a Triangle?
A = ½bh
How do you find the perimeter of a square?
2l + 2w = P
How do you find the perimeter of a triangle?
a + b + c = P
How do you find the area of a rectangle?
l x w = A
