1st Quarter Mid-term review
Name: ____________________________
1. Find the values of x and y. SHOW YOUR WORK!!
x = ___________
.
2x+25
x + 35
y
y = ___________
Using the diagram below, answer questions #2-5.
2. Solve for each angle:
a________
b________
65°
c________
b
a
d________
d
c
115°
e________
f
g
e
f________
27°
g________
3. Name 2 pairs of Vertical Angles using the diagram above.
4. Name 1 pair of Corresponding Angles using the diagram above.
5. Name 1 pair of Same Side Interior Angles using the diagram above.
6. For each diagram find the value of x. Show your work and include the name of the Angle Relationship
you used to solve the problem.
a)
b)
4x + 22
132
3x + 10
x
Show Work
Show Work
Relationship
Relationship
7. Using the diagram below, write one pair of each Angle Relationship in the boxes below.
a
b
d
c
g
e
f
h
corresponding
angles
alternate exterior
angles
Name 1 angle
congruent to f
same-side interior
angles
alternate interior
angles
complementary
angles
supplementary angles
same-side exterior
angles
C
7. Find the measure of C. Show all work.
3x + 4
33
28
A
B
8. Given isosceles triangle ∆LKM with LK = KM…
A. Draw triangle ∆LKM:
B. If L = 5x + 4 and K = 3x + 3, solve for the value of x.
C. Calculate the measure(s) of L, K, and M in degrees? Fill in table below.
Show work:
Angle
L
K
M
Measure
9. Will the lengths 14, 19, and 15 form a triangle? Explain.
10. Write the maximum and minimum values for x as an inequality.
x
6
13
11. For each diagram find the value of x. Show your work.
a)
b)
x
58
41°
x
127°
12. Solve for x in each diagram below:
x
x'
13'
11 in
19'
5 in
13. Find the area of the rectangle to the right.
Round side length to nearest tenth.
14.
Given the area of PQR is 30 in , find length of QR:
15 in
5 in
R
2
P
6
Q
15. Use the Pythagorean Theorem to show whether or not the given lengths of the sides are correct.
12
15
9
16. A balloon floated vertically 25 yards up into the air and then blew west 55 yards.
a. Draw an accurate diagram with labels.
b. Use Pythagorean Theorem to find how far the balloon is from its starting point? Round to the nearest
tenth yard.
17. Consider the right triangle shown below when filling in the table.
A
x°
w
23
B
y
18°
C
Determine whether each expression show in the table is valid (true).
Equation
23
=𝑤
sin 18°
23
= tan 18°
𝑦
cos 𝑥° =
23
𝑤
𝑥° = 𝑠𝑖𝑛−1
𝑤
23
Valid (true)
Not Valid (false)
18. In order to reach the top of a hill which is 300 feet high, one must travel up a straight road 1500
feet to the top.
a. Draw and label a diagram that correctly depicts this situation.
b. Find the angle of elevation for the road. Round answer to the nearest whole foot.
19. Given the triangle shown, fill in the trigonometric ratios for each angle.
A
8
17
B
C
Angle
A
B
C
Sine
15
Cosine
Tangent
20. Use special right triangles to find the area of the square below. (2 points)
6
21. a. Draw the 30/60/90 triangle ∆𝐴𝐵𝐶 below. Label the angles and side lengths.
b. Given that the hypotenuse of ∆𝐴𝐵𝐶 is 14in, find the lengths of the remaining sides.
22. a. Draw the 45/45/90 triangle ∆𝑃𝑄𝑅 below. Label the angles and side lengths.
b. Given that the hypotenuse of ∆𝑃𝑄𝑅 is again 14in, find the remaining sides.
23. a. Draw and label an equilateral triangle with side lengths 10 in.
b. Draw in, and solve for, the height of this triangle.