We included HMH Into Math Grade 8 Answer Key PDF Module 5 Review to make students experts in learning maths.

Vocabulary

continuous
discrete
rise
hypotenuse
leg
run

Choose the correct term from the box to complete each sentence.

Question 1.
In a right triangle, the ____ is the side opposite the right angle, and a ___ is one of the sides that forms the right angle.
Answer: In a right triangle, the hypotenuse is the side opposite the right angle, and a hypotenuse is one of the sides that forms the right angle.

Question 2.
The slope of a non-vertical line is the ratio of the ___ to the ____ between any two points on the line.
Answer: The slope of a non-vertical line is the ratio of the rise to the run between any two points on the line.

Question 3.
The graph of the relationship between the time a train travels and the distance it travels at a constant speed would be a ___ graph.
Answer: The graph of the relationship between the time a train travels and the distance it travels at a constant speed would be a distance-time graph.

Concepts and Skills

Question 4.
Which of these can be used to show that the slope of a non-vertical line is the same anywhere along the line?
A. acute triangles
B. obtuse triangles
C. right triangles
D. any triangles
Answer: D. any triangles

Explanation:
A non-vertical line is a line that, depending on the slope, either falls from the left to the right, is horizontal, or falls from the right to the left. To put it simply, think about finding the slope of any line that is not vertical. Those lines are non-vertical lines.
It is impossible to have any sort of triangle that doesn’t have at least one non-vertical line; this is because the three sides of a triangle connect to form said shape, and multiple non-vertical lines can only exist if they are parallel to each other.

Question 5.
Use Tools The table and the equation each show a proportional relationship between time x, in seconds, and distance y, in meters. Who would finish a 100-meter race faster? How much faster? State what strategy and tool you will use to answer the question, explain your choice, and then find the answer.

y = 8x
x = 3
y = 8(3) = 24 meters
y = 8(5) =  40 meters
y = 5(8) = 64 meters
Therefore Lauren would finish a 100-meter race faster than Amani.

Question 6.
The graph shows right triangles ∆ABC and ∆ADE. The hypotenuse of each triangle lies on the same line.

A. Explain how you know that the triangles are similar.
__________________
__________________
As is seen in the figure ∆ABC and ∆ADE have common angle ∠A.
∆ABC and ∆ADE are right angle triangles.
∠ACB = ∠AED = 90 degrees
Then ∆ABC ∼ ∆ADE

B. How does knowing the triangles are similar help you show that the slope of the line through the hypotenuses is constant?
__________________
__________________
__________________
The slope of the line is ∠A
∠A is constant,
Therefore the slope of the line is constant.

Question 7.
The graph of a proportional relationship is shown.
A. What is the amount Kai earns per hour?
$___ per hour Answer: Answer: 2 hours =$15
1 hour = 15/2 = $7.5 Thus Kai earns$7.5 per hour.

B. Write an equation that relates Kai’s earnings y, in dollars, to x, the number of hours he works.
y = 7.5x

Question 8.
The coordinates of two points are given in the table. Complete the table by giving the coordinates of a third point collinear with the first two points.

m = (y2-y1)/(x2-x1)
m = 4/5
(0, 0) and (5, 4) and third point (a, b)
y = 4/5x + C
0 = 4/5 (0) + C
C = 0
y = 4/5 x
5y = 4x
Let x = 1
5y = 4
y = 4/5
So, the required point is (0, 4/5)

Question 9.
A fire hose sprays 2 gallons of water every 1.5 seconds.
A. Model the relationship between the time in seconds and the amount of water sprayed in gallons with a graph.