Geometry
Topics that Could Appear on Semester 2 Exam
May 14, 2014
Chapter 6

Identify pairs of triangles as similar or congruent, as in problems 6-23, 6-35, 6-47, 6-58, 6-83, and CL 6-101. Expect
students to justify their conclusions using a similarity conjecture (AA ~, SSS ~, SAS ~). In the case of triangles that
are congruent, justifications that use a similarity conjecture with added information that the ratio of similarity is 1 or
that use a triangle congruence conjecture (SSS ≅, ASA ≅, AAS ≅, HL ≅ and SAS ≅) are acceptable.

Use flowcharts to organize arguments about triangle similarity and congruence, as well as to evaluate the logic of
other arguments, as in problems 6-8, 6-23, 6-35, 6-58. 6-63, 6-73, 6-83,CL 6-101, and CL 6-110.

Write the converse of a conditional statement, as in problems 6-48, 6-64, 6-86, and CL 6-100. Students can be
expected to use the converse of parallel line conjectures to determine if two lines are parallel, based on given angle
information. See problem CL 6-102 for an example of this kind of problem.

Master Checkpoint 6: Solving Proportional Equations and Similar Figures, as in problems 6-16, 6-25, 6-37, 6-50, 657, 6-73, and 6-96.
You may also see concepts from previous chapters:

From Chapter 5, the Laws of Sines and Cosines, as in problems 6-15(c), 6-47, 6-55, 6-74(d), and CL 6-105.
Chapter 7:

Construct a proof structured as a flowchart using given information, reasons for each step, and an organized
progression of information, as in problems 7-46, 7-69, 7-76, 7-86, 7-100, 7-108, 7-123, 7-134(a), and CL 7-155. For
example, students might be provided with the parts of a flowchart proof that they need to organize, assessing their
ability to identify if assertions rely on previous facts and how reasons match with statements. Another problem might
ask students to fill in missing steps, while a final problem might ask students to complete a proof that has been started
or to create a proof from scratch.

Work with a simple two-column proof, as in problems 7-113, 7-124, 7-132, and CL 7-148.

Identify different shapes based on a description in words (“must be, could be”) or by their central angle (hinged
mirror), as in problems 7-9, 7-43, 7-55, 7-137, 7-142, 7-144, CL 7-147, and CL 7-156.

Analyze a shape on a coordinate grid, and use information about the length and slope of sides and measures of angles,
to name the shape and justify conclusions, as in problems 7-35, 7-79, 7-131, 7-135, 7-146, CL 7-150, and CL 7-153.

Find the midpoint of segment on a coordinate grid, as in problems 7-20, 7-29, 7-45, 7-119, 7-140, and CL 7-151.

Master Checkpoint 7: Solving with Trigonometric Ratios and the Pythagorean Theorem, as in problems 7-10, 7-15, 734, 7-39, 7-48, 7-85(a), 7-136, and CL 7-152.
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Chapter 8:

Move flexibly around the Regular Polygon Angle Web to find interior angles, exterior angles, or the number of sides
of the regular polygon, given any one of the other pieces of information, as in problems 8-44, 8-53, 8-95, 8-107, 8119, and CL 8-138, and contained in the area problems of the third bullet below. See the Math Notes box in Lesson
8.1.5. Questions on a test could reflect the several different starting places for these problems.

Find missing angles or solve for variables using the sums of interior or exterior angles of non-regular polygons, as in
problems 8-60, 8-61(c), 8-95, 8-97(a), 8-107(a), and CL 8-138.

Find the area of a regular polygon given a side length or radius, as in problems 8-73, 8-84, 8-107(b), 8-105, 8-126, and
CL 8-130. Students develop an algorithm to do this by dividing the polygon into congruent isosceles triangles from a
center point.

Understand how the area and perimeter of similar figures are related, and use those relationships to find areas of
enlarged and reduced shapes, as in problems 8-71(c), 8-83, 8-106(b), 8-123(c), and 8-125(b). Be able to recognize
and use the fact that the ratio of areas of similar figures is the square of the ratio of similarity, and to be able to
calculate the area of an enlarged figure given the area of a smaller figure and a linear scale factor.

Find the area and circumference of circles. Problems may show whole circles alone, or as part of a larger diagram, as
in problems 8-116, 8-123, 8-128, CL 8-130, and CL 8-135. Students can be expected to find the area of sectors of
circles when given a central angle (using proportional reasoning strategies).

Master Checkpoint 8: Angle Relationships in Geometric Figures, as in problems 8-6, 8-23, 8-33, 8-60(a), 8-97(b), 8108, 8-121, 8-124, CL 8-137 and CL 8-139.
Chapter 9:

Represent three-dimensional solids using a side view, a mat plan, and/or a net, as in problems 9-7, 9-21, 9-49, 9-56(a),
9-91, and CL 9-111. Students should also be able to use these representations to calculate the surface area or volume
of the solid.

Find the surface area and volume of three-dimensional shapes, as in problems 9-26, 9-34, 9-38, 9-40, 9-46(a), 9-57, 969, 9-83, 9-95, 9-103, and CL 9-114. Problems can include calculating surface area and volume of three-dimensional
solids composed of cubes, or surface area and volume of prisms and cylinders. Solids can be presented as labeled
pictures, or for added challenge can be described in words.

Find density, as in problems 9-40, 9-57(b), 9-69(d), 9-93(c), and CL 9-114.

Understand and apply the relationship between a linear scale factor and the ratio of areas or ratio of volumes of similar
shapes, as in problems 9-8, 9-20(b), 9-45, 9-46(b), 9-56, 9-91(c), CL 9-112 and CL 9-113(c). Expect students to be
able to find a ratio of areas or of volumes given a linear scale factor. Students should be able to use the ratios to find
side lengths, surface areas, or volumes of similar solids given measurements of one shape in a pair of similar shapes.

Given a ratio of areas or volumes, work backwards to find a linear scale factor, as in problems 9-8(c), 9-86, and CL 9112(b).

Use basic construction techniques to create shapes with specific relationships, as in problems 9-79, 9-80, 9-98, 9-104,
CL 9-110, and CL 9-113(a). Specifically, expect students to be able to use construction techniques to copy angles and
line segments, and to create a perpendicular bisector of a segment and an angle bisector. Problems might ask students
to describe steps to complete simple constructions, as in problem 9-98. Students do not memorize specific
constructions; rather, they justify what they create based on the construction techniques that they apply.

Master Checkpoint 9A: Probability of Unions, Intersections, and Complements, as in problems 9-12(b), 9-36, 9-51,
and 9-73.Master Checkpoint 9B: Exponential Functions, as in problems 9-24, 9-39, 9-61, 9-97, and 9-107.
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Chapter 10:

Understand and use the relationships between central and inscribed angles and their intercepted arcs to calculate arc
and angle measures, as in problems 10-33, 10-68(d), 10-78(b), 10-87, 10-120, and CL 10-185(b). Expect students to
be able to find the measures of both arcs and inscribed and central angles, using information about any one of the
three as a starting place. To connect with earlier topics, problems can ask students to combine their new knowledge
about arcs and angles with their understanding of circumference and circle area in order to calculate arc length and
sector area, as in problems 10-59 and 10-87(c).

Understand and use the facts that an angle inscribed in a semicircle (the angle of a diameter) measures 90°, as in 1043(a) and 10-68(a), and that a line tangent to a circle is perpendicular to the radius of the circle at the point of
tangency, as in problems 10-54, 10-59, and CL 10-185(a).

Understand chord relationships and use those relationships to find the length of a chord. Problems might ask students
to find the length of a segment formed by intersecting chords, as in problems 10-60, 10-78(c), 10-107(b), and CL 10186 or to find the length of a chord given a radius and the measure of an arc or angle, as in problem 10-107 (a).

Use counts, especially in two-way tables, to determine probabilities, conditional probabilities, and association, as in
problems 10-85, 10-101, 10-116, 10-130, and CL 10-188.

Use relative frequencies (probabilities) in two-way tables to determine other probabilities, conditional probabilities,
and association, as in problems 10-102, 10-117, 10-131, 10-176, and CL 10-190.

Use the alternative definition for independence derived from the Multiplication Rule to determine independence, and
vice versa, as in problems 10-131 (d), 10-142, 10-176 (c), and CL 10-190 (b).

Count the number of arrangements using a decision chart, as in problems 10-132, 10-154, 10-155(d), CL 10-187, and
CL 10-189.

Master Checkpoint 10: Angles in and areas of regular polygons, as in problems 10-19, 10-22, 10-70, 10-82, 10-119,
10-156, and CL 10-194.
Chapter 11:

Find Surface Area and Volume of Pyramids, as in problems 11-40, 11-45, 11-52, 11-86, 11-100

Find Surface Area and Volume of Cone, as in problems 11-54, 11-58b

Tangents and Arcs (on circles) – calculate the measure of angles and arcs on a circle formed by chords and tangents
lines, as in problems 11-111, 11-120, 11-124

Secant and Tangent Lines (on circles) – calculate segments lengths and angles formed by two chords, two secant lines,
two tangent lines, or a secant line and tangent line, as in problems 11-104, 11-109, 11-110, 11-117

Surface Area and Volume of Sphere, as in problems 11-72
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