Chapter 2 Ultimate Study Deck

Question 1

What is the Pythagorean Theorem?

Answer 1

a² + b² = c²

Question 2

Distance Formula (1)
(For a horizontal or vertical line)

Answer 2

|B - A|

Question 3

How do you find the distance of a diagonal line

Answer 3

1. Label points
2. Find length of base & height ( a & b )
3. Use Pythagorean Theorem

Question 4

What is zero slope?

Answer 4

When there is no change in the y coordinates
0/1

Question 5

What is vertical/undefined slope?

Answer 5

when there is no change in the x coordinates
1/0

Question 6

How to find slope?

Answer 6

Slope Formula: yB - yA/xB - xA
Basically:
Vertical Change (Change in y)/Horizontal Change (Change in x)

Question 7

What is the Midpoint Formula?

Answer 7

M = (x1 + x2)/2 , (y1 + y2)/2
Used when given two points and asked the midpoint

Question 8

Distance Formula (2)
(Used with Diagonal Lines)

Answer 8

√(x2 - x1)² + (y2 - y1)²

Question 9

How do you prove that two lines are parallel?

Answer 9

Using the slope formula prove that both lines have the same slope.

Question 10

What is the Inverse Property of Addition?

Answer 10

Adding a number and its opposite additive inverse will produce the sum of zero

Question 11

Algebraic Proofs with Parallel Lines

Answer 11

Lines that are parallel have no common points, therefore, if you try to solve for “x” there should be no solution.

Question 12

Slopes of Perpendicular lines have…

Answer 12

opposite reciprocal slopes.
- Change the signs
- Flip the fraction

Question 13

What is literally the best way to find a slope???

Answer 13

y = mx + b
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Question 14

What are Tranversals

Answer 14

A line that intersects two or more lines on the same plane.

Question 15

What is the Corresponding Angles Theorem?

Answer 15

If two parallel lines are cut in half by a transversal line than the corresponding lines are congruent

Question 16

What is the Alternate Interior Lines Theorem?

Answer 16

If two parallel lines are cut in half by a transversal than the alternate interior lines are congruent

Question 17

What is the Alternate Exterior Lines Theorem?

Answer 17

If two parallel lines are cut in half by a transversal line than alternate exterior angles are congruent.

Question 18

What is the Same Side Angles theorem?

Answer 18

If two parallel lines are cut by a transversal than the pairs of same side interior angles are supplementary.
(Equal 180)

Question 19

What is the Perpendicular Bisector Theorem?

Answer 19

If a point lies on the perpendicular bisector of a line segment, the the point is equidistant from the other endpoints of the segment.

Question 20

What is the ratio for midpoints?

Answer 20

1:1 (Line divided into two)

Question 21

What is the Line Ratio Equation?

Answer 21

C = A + ᵃ⁄a+b(B - A)

Question 22

How do you find a random point with a ratio on a slanted line?

Answer 22

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)

Question 23

When trying to find “B” on a slanted line with a given “A” and “C” then-

Answer 23

• take notice of ratio and use Xc = axB +bxA/(a+b)
  You can also use Yc = ayB + byA/(a+b)

Question 24

How do you find the Area of a Triangle?

Answer 24

A = ½bh

Question 25

How do you find the perimeter of a square?

Answer 25

2l + 2w = P

Question 26

How do you find the perimeter of a triangle?

Answer 26

a + b + c = P

Question 27

How do you find the area of a rectangle?

Answer 27

l x w = A