Download spring final review solutions

Name
Date
Per
TOPICS ON FINAL EXAM:

Angle Relationships

Area & Perimeter of a Triangle, Square,

Right Triangle Trigonometry (including
inverse)
Rectangle

Regular Polygon Area

Congruence Properties (SSS, SAS, etc)

Sector Area & Arc Length

Congruent Triangles

Similar Triangles

Converse

Similarity Properties (SAS, ASA, etc)

Distance Theorem

Slope of Parallel & Perpendicular lines

Midpoint of a Line Segment

Special Right Triangles (30-60-90, 45-45-

Polygon Interior Angle Sums

Proving Congruence/Similarity

Triangle Midsegment Theorem

Pythagorean Theorem

Triangle Sum Theorem

Quadrilaterals

Volume & Surface Area of 3D Solids
90)
1. If two sides of a triangle are 5.3 and 10.5, what is the range of lengths for the third side?
Answer:
<x<
V=
2. Determine whether Δ RTK and Δ RTZ can be proved congruent. State the congruence method
you would use: SSS, SAS, ASA, AAS, or HL. If they cannot be proved congruent, state “No
congruence”.
R
RT  KZ
KT  ZT
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K
T
Z
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3. Determine if the triangles are similar. Justify your answer, including the appropriate theorem(s) or
reasons(s) and calculations.
B
6
4
A
8
E
C
3
D
4. Find the perimeter and area of the figure shown. If using decimal answers, round to the nearest
hundredth.
15
10
60o
Perimeter =
Area =
5. Find the value of x.
75
3x
2x
x=
120
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6. The base of a ladder is placed on the ground four feet away from a building. How long must the
ladder be in order for it to reach ten feet up the wall? Round your answer to the nearest hundredth.
Answer:
7. Find the value of x.
xo
x = _______________
9
8
8. Find the value of x.
x
x=
61
32
9. Write the converse of each statement:
a) If you are a student at SVHS, then you love math.
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b) If it is July in Sonoma, then the weather is hot.
10. Write a flow proof, paragraph proof, or two-column proof.
Given: T is the midpoint of SU
T is the midpoint of RV
SR  UV
U
Prove: RST  VUT
R
T
V
S
11. Find the value of x.
x
x = _________
54
12
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12. Find the volume and surface area of the prism.
12
Volume =
Surface Area =
8
6
13. In the regular octagon below, a triangle is drawn in the interior by connecting the center with
two of the vertices, where BC = 8. Find the measure of one interior angle of the octagon, then use
trigonometry to find AD . Find the area of triangle
ABC, then find the area of the octagon.
One interior angle
of the octagon
=
A
AD =
Area of ABC =
B
14.
D
C
Area of Octagon =
a) If a triangle has a base length of 12, what would the height have to be if the area of the
triangle is 36 un2?
b) If the height of a triangle is 10, what would the base have to be if the area of the triangle
is 40 un2?
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15. Find a and b.
a
b
a = _________
b=
6 2
16. Find the value of x and y.
6
y
x=
30
y=
x
17. A regular polygon has 17 sides. Find:
a) the sum of the interior angles
b) the measure of ONE interior angle
c) the measure of ONE exterior angle
18. This drawing shows two parallel lines crossed by a transversal. Solve for x and give the property,
term, or definition that supports your answer.
x = _______________
2x
Reason
(4x-36)
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19. If the area of the square is 100 un2, find the length of the diagonal.
x
20.
a) Name as many CORRESPONDING ANGLE pairs as you can from the figure below.
b) Name as many ALTERNATE INTERIOR ANGLE pairs as you can.
o
c) Name two pairs of SAME-SIDE INTERIOR ANGLES.
m
1 2
3 4
5 6
8 7
n
d) Name as many VERTICAL ANGLE pairs as you can.
\
21.
Find the volume and surface area of the cylinder.
12
8
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22. For the segment with endpoints A (-3 - 9) and B (4,-3) :
a. Find the midpoint of the segment.
b. Find the length of the segment.
c. If point B is the midpoint of AC , name the coordinates of point C.
23.
Identify each figure as specifically as you can based only on the given (marked)
information.
24.
Find the area of a regular pentagon that has a radius of 10 inches.
25 . Find the area of the sector and the length of arc AB.
A
5 cm
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120
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B