We included HMH Into Math Grade 8 Answer Key PDF Module 4 Review to make students experts in learning maths.
HMH Into Math Grade 8 Module 4 Review Answer Key
Vocabulary
In the diagram, Line AF is parallel to Line BE. Give one example of each type of figure in the diagram.
Question 1.
an exterior angle of a triangle _____
Answer: E is an exterior angle of a triangle.
Question 2.
a remote interior angle of Angle BCD ____
Answer: D and C are the remote interior angle of Angle BCD
Question 3.
a transversal of a pair of parallel lines _____
Answer: A and B are the parallel line and H is the line cut by a transversal.
Question 4.
a pair of alternate interior angles formed by a pair of parallel lines and a transversal ____
Answer: a pair of alternate interior angles formed by a pair of parallel lines and a transversal is called alternate exterior angle.
Concepts and Skills
Question 5.
If Triangle ABC is similar to Triangle EDC, which statements about the figures must be true?
A. Angle B measures 70.7°.
B. Angle ACB measures 40.3°.
C. Angle A is the largest interior angle of Triangle ABC.
D. Triangle EDC can be produced from Triangle ABC by a dilation and a reflection.
E. Triangle EDC can be produced from Triangle ABC by a rotation and a dilation.
Answer: D. Triangle EDC can be produced from Triangle ABC by a dilation and a reflection.
Question 6.
In Triangle JKL, ∠J is congruent to ∠L. What is the measure of ∠L? ____
Answer:
Triangle JKL is an isosceles triangle, given that ∠J ≅∠L. An isosceles triangle has two of its angles and sides to be equal.
The exterior angle = 67.8
∠J + ∠L = 67.8
x + x = 67.8
2x = 67.8
x = 33.9 degrees
Thus measure of ∠L is 33.9°
Question 7.
Use Tools A figure with parallel Lines m and n is shown. What are the measures of Angles A, B, and C? State what strategy and tool you will use to answer the question, explain your choice, and then find the answer.
Answer:
Angle A = 53° (alternate angles)
Angle A = Angle B (co-interior angles)
Angle = 143°
37 + C = 180
C = 180 – 37
C = 143°
Therefore, Angle A = 53°
Angle B = 53°
Angle C = 143°
Question 8.
In the figure, Segments SV and RU intersect at Point T. Anna claims that Triangle RST is similar to Triangle UVT. Is Anna’s claim correct? Explain your reasoning.
Answer:
Given,
Segments SV and RU intersect at Point T. Anna claims that Triangle RST is similar to Triangle UVT.
Yes, they are similar triangles because it does not give you a lot of information but it does give you the angles on both sides which is 57 degrees.
Question 9.
What is the value of x in the figure shown? _____
Answer:
104 + y = 180
y = 180 – 104
y = 76
76 + 38 + x = 180
x = 180 – 76 – 38
x = 66 degrees
Question 10.
What is the value of z in the figure shown? ____
Answer:
114.8 + x = 180
x = 180 – 114.8
x = 65.2
45.6 + 65.2 + z = 180
110.8 + z = 180
z = 180 – 110.8
z = 69.2
Question 11.
In the figure, Line a is parallel to Line b.
A. Which equation can be used to determine the value of x?
A. 3x = 2x + 20
B. 90 – 3x = 2x + 20
C. 3x = 180 – 2x + 20
D. 3x + 2x + 20 = 180
Answer:
3x + 2x + 20 = 180
B. What are the values of x and y?
x = ____
y = _____
Answer:
3x + 2x + 20 = 180
5x + 20 = 180
5x = 180 – 20
5x = 160
x = 160/5
x = 32
2x + 20 = y (co-interior angles)
2(32) + 20 = y
y = 64 + 20
y = 84
Question 12.
In the figure. Line l is parallel to Line m. Select all true statements about the figure.
A. g = 54
B. h = 126
C. f = g
D. g + h = 180
E. f = h
Answer:
E. f = h
D. g + h = 180