Download Scope and Sequence CA Geometry Second Edition Library Topic 1

Scope and Sequence
CA Geometry Second Edition Library
The Accelerated Math™ Second Edition California Library scope and sequence is based on extensive
mathematics and standards research. You're sure to find objectives that reinforce the skills you are
teaching, regardless of what instructional materials you use. Accelerated Math makes it easy to
select and organize objectives to suit your textbook and your own teaching approach. This
Accelerated Math library provides the following scope and sequence of objectives:
Topic 1 - Basic Concepts of
Geometry
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Identify a relationship between points,
lines, and/or planes
Determine a length or an angle measure
using the segment addition postulate or the
angle addition postulate
Solve a problem involving a bisected angle
or a bisected segment
Determine the distance between two points
Solve a problem involving the distance
formula
Determine the midpoint of a line segment
given the coordinates of the endpoints
Use coordinates to identify a polygon
Determine the area of a right triangle or a
rectangle given the coordinates of the
vertices of the figure
Solve a problem involving the midpoint
formula
Topic 2 - Parallel and Perpendicular
lines
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Identify angle relationships formed by
multiple lines and transversals
Determine the measure of an angle formed
by parallel lines and one or more
transversals
Identify parallel lines using angle
relationships
Determine the measure of an angle in a
figure involving parallel and/or
perpendicular lines
Determine if lines through points with given
coordinates are parallel or perpendicular
Determine the coordinates of a point
through which a line must pass in order to
be parallel or perpendicular to a given line
Topic 3 - Relationships Within
Triangles
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Topic 4 - Congruent Triangles
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Determine the length of a side or the
measure of an angle in congruent triangles
Identify a triangle congruence postulate
that justifies a congruence statement
Identify congruent triangles using triangle
congruence postulates or theorems
Solve a problem involving a point on the
bisector of an angle
Topic 5 - Quadrilaterals and Other
Polygons
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Determine the measure of an angle using
the sum of the interior angles in a triangle
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Determine the measure of an angle using
angle relationships and the sum of the
interior angles in a triangle
Determine a length in a triangle using a
median
Solve for the length of a side of a triangle
using the Pythagorean theorem
Solve a problem using inequalities in a
triangle
Solve a problem involving two triangles by
using the hinge theorem and other triangle
inequality relationships
WP: Determine a length or an angle
measure using triangle relationships
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Determine the measure of an angle or the
sum of the angles in a polygon
Use the measures of exterior angles to
classify figures and solve problems
Determine a length or an angle measure
using general properties of parallelograms
Determine a length or an angle measure
using properties of squares, rectangles, or
rhombi
Determine a length or an angle measure
using properties of kites
Determine a length or an angle measure
using properties of trapezoids
Determine a length or an angle measure in
a complex figure using properties of
polygons
WP: Solve a problem using the properties
of angles and/or sides of polygons
 2010 Renaissance Learning, Inc .
Scope and Sequence
Topic 6 - Similarity
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Determine the scale factor relating two
similar polygons
Determine the length of a side in one of two
similar polygons
Determine the length of a side or the
measure of an angle in similar triangles
Determine a length given the perimeters of
similar triangles or the lengths of
corresponding interior line segments
Identify a triangle similarity postulate that
justifies a similarity statement
Identify similar triangles using triangle
similarity postulates or theorems
Determine a length in a triangle using a
midsegment
Determine a length using parallel lines and
proportional parts
Determine a length in a triangle given the
bisector of an angle and other lengths
Determine a length using similar triangles
formed by the altitude to the hypotenuse of
a right triangle
WP: Determine a length using similarity
Topic 7 - Right Triangles and
Trigonometry
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Topic 8 - Logical Reasoning and
Proof
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Use inductive reasoning to determine a rule
Use deductive reasoning to draw a valid
conclusion from conditional statements
Identify a statement or an example that
disproves a conjecture
Identify a valid biconditional statement
Determine information that is needed for a
coordinate proof
Complete a proof involving angle or linesegment concepts
Complete a proof involving parallel lines
Complete a proof involving triangles
Complete a proof by contradiction
Complete a proof involving a quadrilateral
Complete a proof involving right triangles
Topic 9 - Circles
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Determine a length in a complex figure
using the Pythagorean theorem
Determine a length using the properties of
a 45-45-90 degree triangle or a 30-60-90
degree triangle
Solve a problem using multiple nontrigonometric right-triangle relationships
WP: Determine a length using the
properties of a 45-45-90 degree triangle or
a 30-60-90 degree triangle
WP: Solve a problem involving a complex
figure using the Pythagorean theorem
Determine a sine, cosine, or tangent ratio
in a right triangle
Determine a length using a sine, cosine, or
tangent ratio in a right triangle
Determine the measure of an angle using a
sine, cosine, or tangent ratio in a right
triangle
WP: Determine a length in a right triangle
using a sine, cosine, or tangent ratio
WP: Determine the measure of an angle in
a right triangle using a sine, cosine, or
tangent ratio
Page 2 of 5
CA Geometry Second Edition Library
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Determine the measure of an arc or a
central angle using the relationship
between the arc and the central angle
Solve a problem involving the length of an
arc
Determine the length of a line segment, the
measure of an angle, or the measure of an
arc using a tangent to a circle
Determine a length using a line segment
tangent to a circle and the radius that
intersects the tangent
Determine a length using two intersecting
tangents to a circle
Determine a length or an arc measure using
the properties of congruent chords
Determine a length using a perpendicular
bisector of a chord
Determine the measure of an arc or an
angle using the relationship between an
inscribed angle and its intercepted arc
Determine the measure of an arc or an
angle using properties of an inscribed
triangle or quadrilateral
Determine the measure of an arc or an
angle formed by intersecting chords or a
chord that intersects a tangent to a circle
Determine the measure of an arc or an
angle formed by two tangents, two secants,
or a tangent and a secant that intersect
outside a circle
 2010 Renaissance Learning, Inc .
Scope and Sequence
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Determine a length using intersecting
chords, two secants that intersect outside a
circle, or a tangent and a secant that
intersect outside a circle
Solve a problem involving intersecting
chords, tangents, and/or secants of a circle
Determine an equation of a circle
Determine the radius, center, or diameter
of a circle given an equation
Determine the area or circumference of a
circle given an equation of the circle
Topic 10 - Area
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Determine the area of a quadrilateral
Determine a length given the area of a
quadrilateral
WP: Solve a problem involving the area of a
quadrilateral
Determine the area of a triangle using
Heron's formula
Determine the area of a regular polygon
Determine a length given the area of a
regular polygon
Approximate the area of a right triangle
using trigonometry
Approximate the area of a regular polygon
using trigonometry
Determine the area of a region formed by
circles within a circle, a polygon within a
circle, or a circle within a polygon
WP: Solve a problem involving the area of a
complex shape formed by circles and
polygons
Determine the area of a sector of a circle
Determine the area of a segment of a circle
Determine the length of the radius or the
diameter of a circle given the area of a
sector
WP: Determine a length or an area
involving a sector of a circle
Determine the measure of an arc or an
angle given the area of a sector of a circle
Solve a problem involving regular polygons
and/or circles that have the same area or
perimeter
Determine the effect of a change in
dimensions on the perimeter or area of a
shape
Determine a probability using an area
model
Page 3 of 5
CA Geometry Second Edition Library
Topic 11 - Surface Area and
Volume
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Determine a length given the surface area
of a right cylinder or a right prism that has
a rectangle or a right triangle as a base
Solve a problem involving the surface area
of a cone or a pyramid that has a rectangle
or right triangle as a base
Determine a length given the surface area
of a right prism or a right pyramid that has
a regular polygon as its base
Determine the volume of an oblique prism
or an oblique cylinder
Determine the volume of a right pyramid or
a right cone
Solve a problem involving the volume of a
right pyramid or a right cone
Determine the volume of an oblique
pyramid or an oblique cone
Determine the surface area of a sphere
Determine the radius, diameter, or
circumference of a sphere given its surface
area
WP: Solve a problem involving the surface
area of a sphere
Determine the surface area of a complex
solid figure
Solve a problem involving the surface area
of a complex solid figure
Determine the volume of a sphere or
hemisphere
WP: Determine the volume of a sphere or
hemisphere
Determine the volume of a complex solid
figure
WP: Solve a problem involving the volume
of a complex solid figure
Determine the effect of a change in the
dimensions of a figure on its volume
WP: Determine the effect of a change in the
dimensions of a figure on its surface area or
volume
Solve a problem involving the surface areas
of similar solid figures
Solve a problem involving the volumes of
similar solid figures
Solve a problem involving two solid figures
that have the same surface area or volume
WP: Solve a problem involving two solid
figures that have the same surface area or
volume
 2010 Renaissance Learning, Inc .
Scope and Sequence
CA Geometry Second Edition Library
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Topic 12 - Transformations in the
coordinate plane
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Relate the coordinates of a preimage or an
image to a translation described using
mapping notation
Determine the coordinates of a preimage or
an image given a reflection across a
horizontal line, a vertical line, the line y =
x, or the line y = -x
Relate the coordinates of a preimage or an
image to a dilation centered at the origin
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Determine the angle of rotational symmetry
of a figure
Determine the coordinates of the image of
a figure after two transformations of the
same type
Determine the coordinates of the image of
a figure after two transformations of
different types
Topic 13 - Constructions
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Determine steps in a geometric
construction
 2010 Renaissance Learning, Inc .
Scope and Sequence
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v. 2.0 02/25/2010
 2010 Renaissance Learning, Inc .