Unit 6 Lesson 4: Parallel and Perpendicular Lines

Question 1

coordinate plane

Answer 1

a two-dimensional plane formed by the intersection of two number lines: the x-axis and the y-axis

Question 2

rise

Answer 2

the number of units you move up or down from point to point; also known as the change in y, or Δy

Question 3

run

Answer 3

the number of units you move left or right from point to point; also known as the change in x, or Δx

Question 3

x-coordinate

Answer 3

the coordinate that identifies the exact location of a point on or parallel to the x-axis

Question 4

slope

Answer 4

the measure of the steepness of a line

Question 5

y-coordinate

Answer 5

the coordinate that identifies the exact location of a point on or parallel to the y-axis

Question 5

How to see if something has a postive slope

Answer 5

The line in the first graph has a positive slope because it goes up from left to right, which illustrates an uphill slope.

Question 6

How to see if something has a negative slope

Answer 6

The line in the second graph has a negative slope because it goes down from left to right, which illustrates a downhill slope.

Question 7

what has a slope of 0

Answer 7

The line in the third graph has no steepness, so it has a slope of 0.

Question 8

What is an example of an undefinded slope

Answer 8

The line in the fourth graph is so steep that it cannot be measured, so it has an undefined slope.

Question 9

how to find the rise and the run

Answer 9

To find the height (or rise) of the ramp you created, you must calculate the difference between the y-coordinates (change in y). To find the length (or run) of that ramp, you must calculate the difference between the x-coordinates (change in x).

Question 10

What is the equation for slope

Answer 10

Mathematically, an expression for the change in y is y2−y1
. Similarly, an expression for the change in x is x2−x1
. The slope of a line is equal to the ratio riserun
, so the formula for finding the slope of any line is change in ychange in x=y2−y1x2−x1=ΔyΔx

Question 11

What is the slope of a line that

Answer 11

the two x-coordinates are the same

Question 12

What happens in a line thats has 2 of the same y-coordinates

Answer 12

a 0 slope because the two y-coordinates are the same.

Question 13

parallel

Answer 13

extending in the same direction, everywhere equidistant and not intersecting

Question 14

parallel lines

Answer 14

a pair of lines on the same plane that never intersect

Question 15

constant

Answer 15

a fixed value in the form of a number or a letter such as a, b, or c

Question 16

coefficient

Answer 16

a number in front of a variable

Question 17

slope-intercept form

Answer 17

the equation y=mx+b
where m is the slope of the line and b
is the y
-intercept

Question 18

proof by contradiction

Answer 18

a method of proving a statement by assuming the statement is false, writing a proof to show that it is false, and then running into a contradiction or impossibility which shows that the statement is in fact true

Question 19

How to prove 2 lines are paralell using proof of contradtion

Answer 19

we want to prove that two distinct lines with the same slope are parallel. To do a proof by contradiction, we will assume that two distinct lines with the same slope are not parallel.

Let l
and n
be two lines with the same slope but are not parallel. Let l
have the equation m=mx+b
. In order for line n
to be parallel to line l
but also be distinct, it must have the same slope but a different y-intercept. Therefore the equation of line n
is y=mx+c
where b≠c
.

Since the lines are not parallel, they have a point of intersection. Find the x
-coordinate of this point by setting the equations equal to each other and solving for x
.

mx+bmx−mx+bb===mx+cmx−mx+cc

This contradicts the condition that b≠c
. Therefore there is no point of intersection, so the lines are parallel.

We have proven that the statement that two distinct lines with the same slope are not parallel is false. Likewise, it has to be true that two distinct lines with the same slope are parallel. This concludes the proof.

Question 20

Angle Addition Postulate

Answer 20

a hypothesis that states that if point D
lies in the interior of ∠ABC
, then m∠ABD+m∠DBC=m∠ABC
If two angles share a common vertex and ray, then the Angle Addition Postulate states that the sum of the measures of the two smaller angles is equal to the measure of the large angle formed by their outer rays.

Question 21

Angle-Angle Similarity Postulate

Answer 21

a hypothesis that states that two triangles are similar if two of their corresponding angles are congruent

Question 22

similar triangles –

Answer 22

triangles that have corresponding sides in the same ratio and have congruent corresponding angles

Question 23

Similar Triangles

Answer 23

Similar triangles are triangles that have the same shape but different sizes. Their corresponding angles are congruent, and their corresponding sides are proportional. For example, if △ABC
and △EFG
are similar triangles, then the following is true:

∠A≅∠E

∠B≅∠F

∠C≅∠G

ABEF=BCFG=CAGE

Question 24

Angle-Angle Similarity Postulate

Answer 24

If two triangles have two pairs of congruent angles, then the Angle-Angle Similarity Postulate states that the two triangles are similar.