Geometry Honors
Review Packet for Final Exam
Name:
Date:
Period:
The focus of the final exam will be the material covered in Semester 2. Material from Semester 1 may be embedded into
questions on the Final Exam. The following is a list of skills that may be assessed on the Final Exam:
Unit 4
 Dilations (Section 6.7 of textbook)
 Identify if a dilation is reduction or enlargement
 Draw a dilation in coordinate plane
 Find scale factor of a dilation
 Find angle measures and lengths of segments in dilations not on coordinate plane
 Similarity (Sections 6.3 and 6.4 of textbook)
 Use properties of dilations to recognize similar figures
 Write and use similarity statements for similar figures
 Find scale factor of similar figures
 Use similar figures to find angle measures and side lengths
 Show triangles are similar using AA~
 Use similar triangles to solve applied problems involving indirect measurement
 Pythagorean theorem (Section 7.1 of textbook)
 Use Pythagorean Theorem to find length of leg or hypotenuse
 Use Pythagorean Theorem to solve real world applied problems
 Special Right Triangles (Section 7.4 of textbook)
 Use the 45°-45°-90° Triangle theorem to find side lengths
 Use the 30°-60°-90° Triangle theorem to find side lengths
 Trigonometric Ratios (Sections 7.5 – 7.7 of textbook)
 Use sine, cosine, and tangent ratios to find side lengths in right triangles (SOHCAHTOA)
 Solve real world problems using SOHCAHTOA (using angles of elevation and depression)
 Use inverse trigonometric functions to find angle measurements in right triangles
 Solve right triangles
 Using the Law of Sines or Cosines to find missing parts of a triangle
Unit 5
 Circle Basics and Properties of Tangents (Section 10.1 of textbook)
 Identify special segments and lines of circles
 Identify and draw common tangents to circles
 Verify a tangent to a circle using theorem 10.1 (page 653)
 Find radius length of circle using theorem 10.1 (page 653)
 Find lengths of tangent segments drawn from a common external point (theorem 10.2 on page
654)
 Measures of Arcs and Angles of Circles (Sections 10.2, 10.4 and 10.5 of textbook)
 Identify and name minor arcs, major arcs, and semicircles
 Find measures of central angles, minor arcs, major arcs, and semicircles
 Determine if arcs are congruent
 Find measures of inscribed angles (theorem 10.7 on page 672)
 Find measures of angles of quadrilaterals inscribed in a circle (theorem 10.10 on page 675)
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 Find measures of angles and arcs formed by a tangent intersecting a chord at a point on the
circle (theorem 10.11 on page 680)
 Find measures of angles and arcs formed by chords that intersect inside the circle (theorem
10.12 on page 681)
 Find measures of angles and arcs formed by intersecting tangents and secants outside the circle
(theorem 10.13 on page 681)
Find Segment Lengths in Circles (Section 10.6 of textbook)
 Find lengths of segments formed by intersecting chords in a circle (theorem 10.14 on page 689)
 Find lengths of segments formed by intersecting secants or intersecting secants and tangents
outside a circle (theorems 10.15 and 10.16 on pages 690-691)
 Solve real world applications involving intersecting secants or intersecting secants and tangents
similar to Example 4 on page 692
Find Circumference and Arc Length (Section 11.4 of textbook)
 Find the circumference of a circle
 Use circumference to find distance traveled (see Example 2 on page 747)
 Find length of an arc
 Find length of an arc in radians
 Use arc length to find angle or arc measures
 Use arc length to find angle or arc measures in radians
 Use arc length to find perimeter of composite figures
Find Areas of Circles and Sectors (Section 11.5 of textbook)
 Find area of a circle
 Find area of sector
 Find area of sector in radians
 Use the area of sector to find length of radius, area of circle, or measures of angles or arcs in
circles
 Find area of composite figures
Radian Measure (Notes worksheet, not covered in textbook)
 Convert degree measures to radian measures
 Convert radian measures to degree measures
Write and Graph Equations of Circles (Section 10.7 of textbook)
 Write equation of circle in standard form
 Write equation of circle in standard form by completing the square
 Identify center and radius of circle given equation in standard form
 Graph a circle in the coordinate plane
 Prove or disprove that a point lies on a circle
 Use graphs of circles to solve real world problems
Unit 6
 Volume of Solid Figures (Sections 12.4 – 12.6 of textbook
 Find volume of prisms, cylinders, pyramids, cones, spheres.
 Use volume formulas to find volumes of composite figures.
 Use volume formulas to find missing dimensions of solids.
 Use volume formulas to solve applied problems.
Practice Problems
1. If two polygons are similar then what must be true about the corresponding angles and corresponding
sides? (Lesson 6.3)
2. ABC and XYZ are similar with A = X, and B = Y. If AB, BC, and AC are 7 inches, 9 inches, and 10
inches, respectively, and XY is 9 inches, find XZ. (Lesson 6.3)
3. Determine whether the figures are similar. (Lesson 6.3)
4. The hexagons below, ABCDEF and JKLGHI, are similar. If CD = 6, LG = 9, and the perimeter of ABCDEF is
40, what is the perimeter of JKLGHI? (Lesson 6.3)
5. A building casts a shadow 174 meters long. At the same time, a pole 5 meters high casts a shadow 15
meters long. What is the height of the building? (Lesson 6.4)
6. Jimmy wants to find the height of the tallest building in his city. He stands 422 feet away from the
building. There is a tree 40 feet in front of him, which he knows is 22 feet tall. How tall is the building?
(Round to the nearest foot.) (Lesson 6.4)
7.
Are the triangle below similar? (Lesson 6.4)
8. Find the Scale factor from A to B
9. Find the scale factor.
Find the unknown side length of the right triangle using the Pythagorean Theorem or a Pythagorean triple.
(Lesson 7.1)
10.
11.
12.
13. A ladder is leaning against a house. The ladder is 13 feet long and the foot of the ladder is 5 feet away
from the base of the house. How far up the side of the house does the ladder reach? (Lesson 7.1)
Find the value of each variable. Write your answers in simplest radical form. (Lesson 7.4)
14.
15.
16. A biologist is standing 50 feet from the base of a large oak tree. The biologist measures the angle between the
ground and the top of the tree to be 57°. Find the height h of the oak tree to the nearest foot. (Lesson 7.5)
Find the value of x. Round your answers to the nearest tenth. (Lessons 7.5 and 7.6)
17.
18.
19. You need to determine the area of a garden which is in the shape of a right triangle. The hypotenuse measures
25 feet and one of the acute angles measures 36°. Round your answer to the nearest tenth. (Lesson 7.6)
Use a calculator to approximate the measure of A to the nearest tenth of a degree. (Lesson 7.7)
20.
21.
Find the value(s) of the variable. Points B and D are points of tangency.(Lesson 10.1)
22.
23.
Tell whether the given arcs are congruent. Explain why or why not. (Lesson 10.2)
24. JL, MK
25. AB, DE
Find the values of the variables. (Lesson 10.4)
26.
27.
28.
Find the values of x (Lesson 10.5)
29.
30.
Find the value of x. (Lesson 10.6)
31.
32
33.
Find the areas of the sectors formed by DFE. Round answers to the nearest tenth. Also find the
length of arc DE. (Lesson 11.4/11.5)
34.
35.
36. How can you convert a radian measure to degrees?
37. How can you convert a degree measure to radians?
38. Convert 40˚ to radians.
11𝜋
39. Convert
radians to degrees
3
Use the given information to write the standard equation of the circle. (Lesson 10.7)
40. The center is (–3, 2) and a point on the circle is (5, 2).
41. The center is (6, –1) and a point on the circle is (–1, 6).
42. Nicole is buying an aquarium in the shape of a rectangular prism and measures 3.5 feet by 4 feet by 4 feet.
What is the volume of the aquarium?
43. The volume of the pyramid below is _____.
44. Describe what happens to the volume of a cone if its radius is doubled while its height is halved. The
volume is _____.
[A] unchanged
[B] doubled
[C]
increased by a factor of
[D] not able to be determined
45. A machinist drilled a conical hole into a cube of metal
as shown. If the cube has sides of length 8 cm, what is the
volume of the metal after the hole is drilled?
and round to the nearest tenth.
46. The base of the pyramid below is a non-regular heptagon
with an area of 30.0 square yards. The height of the pyramid
is 6.6 yards. Find the volume of the pyramid.
47. Find the volume of the figure to the nearest tenth.
48. Find the volume, to the nearest cubic foot, of a sphere whose surface area is 100
.
49. A sphere fits snugly inside a right cylinder as shown below. Find the volume lying outside the sphere but inside
the cylinder to the nearest tenth of a cubic inch.
50. Determine whether the dilation from Figure A to Figure B
is a reduction or an enlargement. Then find its scale factor.
51. C'O'B' is the dilation image of COB about the origin.
What is the scale factor and what are the coordinates of C’?
y
C (0, 4)
C'
B (-10, 0) B' (-6, 0)
O
x