Download Geometry CP Final Exam Review Packet 2021 and more Summaries Geometry in PDF only on Docsity!
Name: Review for Final 2021 Period: Geometry CP Note to student: This packet should be used as practice for the Geometry CP Final Exam. This should not be the only tool that you use to prepare yourself for the exam. You must go through your notes, re-do homework problems, class work problems, formative assessment problems, and questions from your tests and quizzes throughout the year thus far. Section 1 1) Classify each statement as true or false, and explain your reasoning in each false case.
a) Two planes intersect in only one point. __________________________________
b) A ray starts at one point on a line and goes on forever. ______________________
c) The intersection of 2 planes is one line __________________________________
d) Any four points are collinear. __________________________________________
2) Use the figure below for #6- 14. Note that 𝑅𝑁⃡ pierces the plane at N. It is not coplanar with V.
a) Name two segments shown in the figure. b) What is the intersection of 𝑪𝑴⃡ and 𝑹𝑵⃡? c) Name three collinear points. d) What are two other ways to name plane V? e) Are points R, N, M, and X coplanar? f) Name two rays shown in the figure. g) Name the pair of opposite rays with endpoint N. h) AN is the same as NA. True or False? i) ANX names a plane. True or False?
- Below each figure write the name of the kind of rigid transformation shown. a. b. c.
___________________ ___________________ ________________
A B C
Section 2 Complete the following statements:
ABC and BCD are complementary. mABC =6xo^ and mBCD = 12xo. Find x.
ABC and BCD are supplementary. mABC =40xo^ and mBCD = 20o. Find x.
AB = 2 x + 1, BC = 16 inches, AC = 5 x – 4. Use
the diagram to solve for x :
Solve for y : m∠DGF =12 y – 5, m∠EGF = 24o, m∠DGE = 5 y + 6
𝑊𝑆 bisects BWV. mBWS = 32o. What is mBWV?
Determine the value of 𝑥:
a) b) c) d)
- Use the following steps to determine whether the given statement is a definition.
Linear pairs are supplementary, adjacent angles. a) Conditional statement
b) Converse
c) Biconditional statement d) Decide whether the statement is a definition. Explain your reasoning.
G
F
E
D
50 o^2 x + 20
112 o
x
- Fill in the blanks so that the sentences are true.
a) The sum of angles in any quadrilateral is _________________.
b) In a parallelogram diagonals ____________________________________________ and opposite angles are
c) ________________________________________.
d) A _______________ and a ___________________ have perpendicular diagonals.
e) A __________________________________ is a quadrilateral with only one pair of parallel sides.
f) A square is a quadrilateral with _________________ congruent sides and _________________ right angles.
g) A rhombus is a ____________________________ with four ___________________________ sides.
h) A __________________________________________ is a quadrilateral with 2 pairs of parallel sides.
i) Any four-sided polygon is a _______________________________________________________________.
j) A rectangle is a quadrilateral with _________________________________________________________.
- Polygon DEFG is a parallelogram. GF = 3 in, DG = 2 in, m∡GDE = 110o
a) m∡DGF = _____________ c) 𝐸𝐹̅̅̅̅ = _____________
b) m∡GFE = _____________ d) 𝐷𝐸 ̅̅̅̅̅ = _____________
- MNOP is a rhombus. If m MNO 88 , find each of the following:
a) m NOP ________
b) m OPG ________
c) m OGN ________
- Parallelogram RUST
G
D E
F
P
M N
O
G
___ 58 ___ ___ 30 ___ ___ 9 ___
_________ ___ 28 ___ _________
_________ _________ _________
_________ _________ _____
m RUS RU cm RQ cm m UST US cm QS m STR ST TQ m TRU TR QU
____
RS _________ UT ___ 50 cm ___
Polygon ABCD is a rhombus. AB = 4x + 2 and AD = 30. What is x? Give a reason for your equation.
Polygon ABCD is a rectangle. 𝐴𝐶̅̅̅̅ and 𝐵𝐷̅̅̅̅ intersect to E. AE = 12 ft. What is BD?
Use trapezoid TRAP to the right to answer the following:
If 𝑚∠𝑇 = 60° find the measures of the other angles.
m R ________ m A ________ m P ________
- Find the following.
a) NM = _______________ b) x = _______________
c) What is NM called?_____________________________________
- Find the slope, midpoint , and length of each of the following segments whose endpoints are given.
a) (-1, 4) and (4, 10) b) (8, 0) and (10, 6)
- Lines that are parallel have ____________ slopes and lines that are perpendicular have ______________ slopes.
G
I
H
N M
32 - 52x 120
A B
D C
- Label and sate what additional information is required in order to know that the triangles are congruent for the reason given.
a) b) c)
- Determine whether or not the triangles below are similar (you may need to do a little work to figure it out) by AA, SSS, or SAS, or none of them. If they are similar, complete the similarity statement.
a) b) c)
ABC ~ ABC ~ CBA ~
d) e) f)
LVM ~ TUV ~ WXY ~
- Determine whether the polygons are similar, not similar, or not enough information given. If they are similar, determine the scale factor comparing the first to second figure.
a) b) c)
- The following polygons are similar; find x and y.
a) b)
54 o 1 2
3 y°
2x – 1
x
x + 2 5 5 8
y
(^) AFN ~ DPG , AF = 2 cm., FN = 3 cm., DG = 10 cm., and PD = 8 cm. Find AN. If m∠A = 36°, what is m∠D?
Use the following image to explain why the two triangles are similar, then estimate the length of the lake.
10) Solve for x.
a) b) c)
- Use the diagram to find the height of each building.
a) b) c)
Section 5
- For # 1-3 two lengths of the right triangle are given. Find the missing length.
a) a = 13 b = __________ c = 14
b) a = 12 b = 16 c =_________
c) a = ________ b = 7 c = 13
a
c
b
x
x
x
30 ft 40 ft
36 ft 24 ft
16 ft 12 ft 18 ft
24 ft
20 ft
8 ft
20 ft
14 ft
12 ft
- Find the area of the following figures.
a) b) c)
d) e) f)
- Find the circumference AND area of each figure. Leave your answer in terms of π.
a) r = 8 mm b) d = 26 cm c)
- Round your answers to 7 a) to the nearest hundredth.
C = _______________________ A = ______________________
- Find the radius of each circle from the given information. Round to the nearest tenth if necessary.
a) Area = 256π in^2 b) Circumference = 120 ft
r = ________ r = ________
If the area of a parallelogram is 100 cm^2 and the length of the base is 25 cm, what is the height?
If the area of a parallelogram is 45 ft^2 and the height is 3 ft, what is the length of the base?
If the area of a trapezoid is 250 in^2 , the lengths of the bases are 23 in and 27 in, what is the height?
If the area of a triangle is 343 u^2 and the height is 14 u, what is the length of the base?
Find the area of the shaded region.
Find the area of the composite figures below.
a) b)
Section 6
- For the following, refer to the solid below.
a) Name the solid.______________________ b) Name a pair of parallel planes. ____________________ c) Name two segments skew to BF ___________________ d) Name two segments to plane BFD.________________ e) What is the volume of the solid if BC = 4, AC = 3, and DC = 2.
- What is the slant height of a right cone with a radius of 8 in. and a height of 14 in. ________
F
E D
C
B
A
km
- The surface area of a square pyramid is given by 540 cm^2 and the side of the square is 10 cm. Find the slant height of the square pyramid.
5) The volume of a cylinder is 960 cubic inches. The height of the cylinder is 15 inches. Find the radius.
6) If a cylinder has surface area of 128 sq ft, and the height of the cylinder is 12 feet, find the radius and the
volume.
7) The volume of a spherical ball is 5,000 cm^3. What is the radius of the ball?
Section 7
1) Find the degree measures of each arc or angle by using the central angle measures given in ⨀𝑀
a) 𝑚𝐴𝐶̂ ______________ b) 𝑚𝐹𝐴̂ _____________ c) 𝑚𝐶𝐵𝐹̂ _____________ d) 𝑚𝐷𝐵̂ _____________ e) 𝑚𝐴𝐷𝐶̂ _____________ f) 𝑚𝐷𝐶𝐴̂ ____________ g) 𝑚∡𝐷𝑀𝐶__________
2) Determine arc with length L of a circle with radius 8.5 in and degree measure 240 °.
3) Each polygon circumscribes a circle. What is the perimeter of each polygon?
a. b. c.
A 86 o 34 o
70 o^84 o M
B
C
D
F
Using circle O below, name the following: a. Diameter b. Central Angle c. Minor Arc d. Major Arc e. Semicircle f. Radius g. Tangent h. Point of Tangency
For the following, in ⨀𝑀, AC is the diameter, 𝐷𝐶 is tangent to the circle at point C , and 𝑚𝐵𝐶̂ = 78 𝑜.
a) m BAC ____________ b) m BEC ____________ c) 𝑚𝐴𝐵̂ ____________ d) m ACB ____________ e) m ABC ____________ f) m ACD ____________
g) ________ is a minor arc, _______ is a major arc h) _________ is a radius, 𝐴𝐶̅̅̅̅ is a _____________________. i) 𝐶𝐷⃡ is a ______________________
- What is the value of x? Lines that appear to be tangent are tangent. Round to the nearest hundredth if necessary. a) b) c) d)
M
B
A
E
D
C
H K
D
C
O
A
F
L
B
E
G
Section 8
1) Using the triangles below, determine the trigonometric ratio. Leave your answers as simplified fractions.
a) tan B = ________ b) cos A = __________ c) sin F = ________ d) tan G = __________
- Find the marked side of each of the following triangles.
a) b) c) d)
- Find the value for each of the marked angles.
a) b) c) d)
4) A skateboarding ramp is 12 in. high and rises at an angle of 17 . How long is the base of the ramp? What
is the length of the ramp? Round your answer to the nearest inch.
- Joey is walking home from the library. He can walk for 1 mile along the street, then turn right and walk 1.
miles along another street; or he can cut across a large field straight to his house. At what angle, , should
he head off from the library, and how far, d , should he cut across the field?
=__________________
d = __________________
C
A
B
F
H
G
C
L
H
d
1 m
1.5 m
A
D
B
C
Q
S R
P T
Proofs
- Given: B and^ D are right angles,^ AB^ CD
Prove: DAC^^ BCA
A
B
C D
E
Given: 𝐴𝐶̅̅̅̅ ≅ 𝐸𝐶̅̅̅̅ , 𝐵𝐶̅̅̅̅ ≅ 𝐷𝐶̅̅̅̅ Prove:CBACDE
Given: is the midpoint of , Prove:
Q PR P QRT
SQP TQR
