Mathematics - Geometry
2010
KEY ELEMENTS
CONTENT
PERFORMANCE TARGETS
(What Students should know)
(What Students should be able to do)
Common Core State Standards
GEOMETRY
Congruence
Experiment with transformations in the plane
1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance
along a line, and distance around a circular arc.
2. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in
the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g.,
translation versus horizontal stretch).
3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
5. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry
software. Specify a sequence of transformations that will carry a given figure onto another.
Understand congruence in terms of rigid motions
6. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures,
use the definition of congruence in terms of rigid motions to decide if they are congruent.
7. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and
corresponding pairs of angles are congruent.
8. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
Prove geometric theorems
9. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior
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Mathematics - Geometry
2010
KEY ELEMENTS
CONTENT
PERFORMANCE TARGETS
(What Students should know)
(What Students should be able to do)
angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant
from the segment’s endpoints.
10. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are
congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at
a point.
11. Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a
parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
Make geometric constructions
12. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding,
dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines,
including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
13. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Similarity, Right Triangles, & Trigonometry
Understand similarity in terms of similarity transformations
1. Verify experimentally the properties of dilations given by a center and a scale factor:
A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
2. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity
transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all
corresponding pairs of sides.
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Mathematics - Geometry
2010
KEY ELEMENTS
CONTENT
PERFORMANCE TARGETS
(What Students should know)
(What Students should be able to do)
3. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Prove theorems involving similarity
4. Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the
Pythagorean Theorem proved using triangle similarity.
5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Define trigonometric ratios and solve problems involving right triangles
6. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for
acute angles.
7. Explain and use the relationship between the sine and cosine of complementary angles.
8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Apply trigonometry to general triangles
9. (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
10. (+) Prove the Laws of Sines and Cosines and use them to solve problems.
11. (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying
problems, resultant forces).
Circles
Understand and apply theorems about circles
1. Prove that all circles are similar.
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Mathematics - Geometry
2010
KEY ELEMENTS
CONTENT
PERFORMANCE TARGETS
(What Students should know)
(What Students should be able to do)
2. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed
angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
4. (+) Construct a tangent line from a point outside a given circle to the circle.
Find arc lengths and areas of sectors of circles
5. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the
angle as the constant of proportionality; derive the formula for the area of a sector.
Expressing Geometric Properties with Equations
Translate between the geometric description and the equation for a conic section
1. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a
circle given by an equation.
2. Derive the equation of a parabola given a focus and directrix.
3. (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
Use coordinates to prove simple geometric theorems algebraically
4. Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the
coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).
5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or
perpendicular to a given line that passes through a given point).
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Mathematics - Geometry
2010
KEY ELEMENTS
CONTENT
PERFORMANCE TARGETS
(What Students should know)
(What Students should be able to do)
6. Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
Geometric Measurement & Dimension
Explain volume formulas and use them to solve problems
1. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection
arguments, Cavalieri’s principle, and informal limit arguments.
2. (+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.
3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Visualize relationships between two-dimensional and three-dimensional objects
4. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of
two-dimensional objects.
Modeling with Geometry
Apply geometric concepts in modeling situations
1. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
2. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).
3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with
typographic grid systems based on ratios).
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Mathematics - Geometry
2010
KEY ELEMENTS
CONTENT
PERFORMANCE TARGETS
(What Students should know)
(What Students should be able to do)
 Name and sketch geometric figures
 Apply segment postulate to identify congruent
segment
 Students will model points, lines, and planes using
foam trays and uncooked spaghetti. They will explore
intersections of lines, and planes.
 Find midpoint of segments in the coordinate plane
 Find lengths of segments in the coordinate plane
ESSENTIALS OF GEOMETRY
 Identify Points, Lines, and Planes
 Use Segments and Congruence

Use Midpoint and Distance Formulas
FOLD A SEGMENT BISECTOR
Geometry McDougal Littell P. 15
Students will draw a line segment AB on paper, fold the
paper so that the two points fall on top of each other,
label the point M and compare the segments AM and
MB, and AB.
MODIFICATIONS
Using Geometer’s Sketch-pad students will:

Construct Acute, Right, Obtuse, and Straight angles

Explore Protractor Postulate

Explore The Angle Addition Postulate


Describe Angles Pair Relationship
Classify Polygons
 Use special angle relationships to find angle
measures.
 Classify polygons
 CONSTRUCT REGULAR POLYGONS
 Use the compass tool of the Geometer’s Sketchpad
to construct a circle and an inscribed square.
Using Geometer’s Sketch-pad students will:
1. Construct various polygons; triangle, square,
pentagon, etc
2. Measure sum of interior angles
3. Develop a formula for sum of angles in a polygon of
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Mathematics - Geometry
2010
KEY ELEMENTS
CONTENT
PERFORMANCE TARGETS
(What Students should know)
(What Students should be able to do)


Perimeter, Circumference, and
Area
PARALLEL AND PERPENDICULAR LINES
 Identify Pairs of Lines and Angles
 Parallel Lines and Transversals
 Prove Lines are Parallel
 Find and Use Slopes of Lines
 Prove theorems about Perpendicular
lines
a given
number of sides
Students will be able to:
 Find dimensions of a polygon
 Find Perimeter
 Find Circumference
 Find Area
Using a Graphing Calculator students will:
1. Construct different rectangles of area 36 square
units but of different dimensions.
2. Plot the various dimensions that produces the
same area and make observations.
INVESTIGATE SLOPES
Use Geometer’s Sketchpad to verify the equality of slopes
of parallel lines
Students will be able to:
 Identify angle pairs formed by three intersecting
lines
 Use angles formed by parallel lines and transversals
 Using Geometer’s Sketch-pad, Students will draw
two parallel lines and a transversal and explore the
relationship among angles formed.
 Use angle relationships to prove that lines are
parallel
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Mathematics - Geometry
2010
KEY ELEMENTS



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
CONGRUENT TRIANGLES
Apply Congruence and Triangles
Prove Triangles Congruent
Use two more methods to prove
congruence
Congruent triangles
Isosceles and Equilateral Triangles



CONTENT
PERFORMANCE TARGETS
(What Students should know)
(What Students should be able to do)
Classify triangles by side and by angles
Find measures of angles algebraically
Understand congruence transformations
 Students will review key vocabulary and theorems
 Solve algebraic problems on geometry concepts
 Find and compare slopes of lines
 Find equations of lines
 Students will review key vocabulary and theorems
 Write equations of parallel lines and graph them
 Write equations of perpendicular lines and graph
them
 Students will review key vocabulary and theorems
 Apply theorems learned in section to solve
algebraic problems
Students will be able to:
 Identify congruent figures
 Use side lengths to prove triangles are congruent
 Classify triangles by side and by angles
 Find measures of angles algebraically
 Classify triangles by side and by angles
 Find measures of angles algebraically
DISCOVERING ASA CONGRUENCE
Students will use tracing paper and straightedge to
investigate congruence of triangles by Angle-Side-Angle
COMPARING CONGRUENT TRIANGLES
Students will use ruler and protractor to construct two
congruent triangles and compare corresponding parts
Students will be able to:
 Use theorems about isosceles and equilateral
triangles
 Create an image congruent to a given triangle
INVESTIGATE SLIDES AND FLIPS
Students will investigate reflection and rotation on a
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Mathematics - Geometry
2010
KEY ELEMENTS
CONTENT
PERFORMANCE TARGETS
(What Students should know)
(What Students should be able to do)
coordinate axis.
RELATIONSHIPS WITHIN TRIANGLES
 Midsegment Theorem and
Coordinate Proof
 Perpendicular Bisectors
INVESTIGATE SEGMENTS IN TRIANGLES
Students will use Geometer’s Sketchpad to investigate
whether or not the midsegments of a triangle relates to
the sides of a triangles
Students will be able to:
 Use properties of midsegments and write
coordinate proofs
 Use the midsegment theorem to find lengths
 Place figure in a coordinate plane
 Use perpendicular bisectors to solve problems

Angle Bisectors of Triangles
EXPLORING PERPENDICULAR BISECTORS
Students will use tracing paper and straightedge to
investigate the relationship between the points on a
perpendicular bisector of a segment and the endpoint of
that segment
EXPLORING THE INCENTER
Students will use tracing paper, straightedge, and compass
to explore the relationship between the incenter and the
sides of a triangle


Medians and Altitudes
Inequalities in a Triangle
Students will be able to:
 Use angle bisectors to find distance relationships
 Use medians and altitudes of triangles
 Use the angle bisector theorem
 Use the concurrency of angle bisectors
INVESTIGATING MEDIANS AND ALTITUDES
Students will use Cardboards to investigate the relationship
between segments formed by the medians of a triangle
Students will be able to:
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Mathematics - Geometry
2010
KEY ELEMENTS
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

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

Inequalities in two Triangles and
Indirect Proof
SIMILARITY
Ratios, Proportions, and the
Geometric Mean
Proportions to solve Geometry
Problems
Similar Polygons
Prove Triangles Similar by AA
Prove Triangles Similar by SSS and
SAS
CONTENT
PERFORMANCE TARGETS
(What Students should know)
(What Students should be able to do)
 Use medians and altitudes of triangles
 Find possible side lengths of a triangle
 Use the centroid of a triangle
 Find centroid of a triangle
DISCOVERING THE HINGE THEOREM
Students will use tracing paper and straightedge to
investigate triangles with two congruent sides
Students will be able to:
 Use inequalities to make comparisons in two
triangles
 Use the hinge theorem and its converse
 Write an indirect proof
INVESTIGATING THE CROO PRODUCTS PROPERTY
Students will investigate the cross product property by
equating the products of means and extremes
Students will be able to:
 Solve problems by writing and solving proportions
 Use the extended ratios and simplify ratios
 Find geometric means
INVESTIGATE PROPERTIES OF PROPORTIONS
Students will rearrange numbers to create proportions
Students will be able to:
 Use proportions to solve geometry problems
 Use proportions to identify similar polygons
 Use properties of proportions
 Find the scale of a drawing
SIMILAR POLYGONS
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Mathematics - Geometry
2010
KEY ELEMENTS
CONTENT
PERFORMANCE TARGETS
(What Students should know)
(What Students should be able to do)
Students will use Geometer’s Sketchpad to compare sides
and angles of a figure and its reduced version
Students will be able to:
 Use proportions to identify similar polygons
 Use the AA Similarity Postulate
DISCOVERING TRIANGLE SIMILARITY SHORTCUTS
Students will use straws and tape to show that
corresponding sides of similar triangles are proportional


Use Proportionality Theorems
Similarity Transformations
RIGHT TRIANGLES AND TRIGONOMETRY
 Apply the Pythagorean Theorem
Students will be able to:
 Use the SSS and SAS Similarity Theorems
 Use the similarity postulate
 Use indirect measurement
INVESTIGATE TRIANGLES & CONGRUENCE
Students will use a graphing calculator to compare segment
lengths in triangles
Students will be able to:
 Use proportions with a triangle or parallel lines
 Find the length of a segment
 Determine whether line segments are parallel
PERFORM SIMILARITY TRANSFORMAIONS
Students will use Geometer’s Sketchpad perform
transformations

Draw a dilation

Find a point on a dilation
PYTHAGOREAN THOEREM
Students will use graph paper to explore the relationship
among sides of a right triangles

Solve problems on side lengths in right triangles
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Mathematics - Geometry
2010
KEY ELEMENTS







Converse of the Pythagorean
Theorem
Similar Right Triangles
Similar Right Triangles
Special Right Triangles
Apply the Tangent Ratio
Sine and Cosine Ratios
Right Triangles
CONTENT
PERFORMANCE TARGETS
(What Students should know)
(What Students should be able to do)
CONVERSE OF THE PYTHAGOREAN THEOREM
Students will use graphing calculator to explore
relationship between sides and angles of a triangle
Students will be able to:

Use the converse of the Pythagorean theorem to
determine if a triangle is a right triangle

Use properties of the altitude of a right triangle

Solve problems on similar right triangles
SIMILAR RIGHT TRIANGLES
Students will explore how geometric means are related to
the altitudes of a triangle
Students will be able to:

Use properties of the altitude of a right triangle

Use the relationships among the sides in special
right triangle
RIGHT TRIANGLE RATIO
Students will use Geometer’s Sketchpad establish formulas
for the trigonometric ratios
Students will be able to:

Use the relationships among the sides in special
right triangle

Use the tangent ratio for indirect measurement
APPLY SINE AND COSINE RATIOS
Students will use Geometer’s Sketchpad explore the
relationship between sides of a triangle
Students will be able to:

Use the sine and cosine ratios
SOLVING REAL – WORLD PROBLEMS USING
TRIGONOMETRY
Students will use a calculator to find an angle measure in a
right triangle given two sides
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Mathematics - Geometry
2010
KEY ELEMENTS
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




QUADRILATERALS
Angle Measures in Polygons
CONTENT
PERFORMANCE TARGETS
(What Students should know)
(What Students should be able to do)
Students will be able to:

Use inverse tangent, sine, and cosine ratios
INVESTIGATE ANGLE SUMS IN POLYGONS
Generator CD
Activity 8.1
Students will derive a formula for the sum of the measures
of the interior angles of a convex n-gon
Ties of Parallelograms
Show that a quadrilateral is a
parallelogram
Students will be able to:

Find angle measures in polygons

Find the sum of angle measures in a polygon

Find the number of sides of a polygon
INVESTIGATE PARALLELOGRAMS
Students will use Geometer’s Sketchpad to investigate
some of the properties of parallelograms
Properties of rhombuses, rectangles,
and squares
Students will be able to:

Find angle and side measures in parallelograms

Use properties to identify parallelograms

Use the properties of a parallelogram

Find the intersection of diagonals
EXPLORING PROPERTIES OF RHOMBUSES
Students will explore the properties of a rhombus
Properties of Trapezoids and Kites
Special Quadrilaterals
Students will be able to:

Use properties of rhombuses, rectangles, and
squares

Use Properties of Trapezoids and Kites

Use properties of special quadrilaterals

Classify special quadrilaterals
MIDSEGMENT OF A TRAPEZOID
Students will use Geometer’s Sketchpad explore the
properties of the midsegment of a trapezoid
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Mathematics - Geometry
2010
KEY ELEMENTS
CONTENT
PERFORMANCE TARGETS
(What Students should know)
(What Students should be able to do)
Students will be able to:

Use Properties of Trapezoids and Kites

Identify special quadrilaterals

Use a coordinate plane
PROPERTIES OF TRANSFORMATIONS
 Translate Figures and Use Vectors



Properties of Matrices
Perform reflections
Perform Rotations
COMPARING TRANSLATED POLYGONS
Students will use Geometer’s Sketchpad to investigate
what happens to a triangle when a constant is added to its
x and y coordinates
Students will be able to:

Use a vector to translate a figure.

Translate a figure in coordinate plane

Write a rule for transformation
INVESTIGATING MATRIX ADDITION & TRANSFORMATIONS
Students will use Geometer’s Sketchpad to investigate the
effect matrix addition has on the coordinates of a triangle
Students will be able to:

Perform translations using matrix operations

Add and subtract matrices

Represent a transformation using matrices
REFLECTION IN THE PLANE
Students will use Geometer’s Sketchpad to explore the
relationship between the line of reflection and the segment
connecting a point and its image
Students will be able to:

Reflect a figure in any given line

Graph reflection in horizontal and vertical lines

Use matrix multiplication to reflect polygons
EXPLORING ROTATIONS ABOUT THE ORIGIN
Students will use Geometer’s Sketchpad to explore
rotations about origin
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Mathematics - Geometry
2010
KEY ELEMENTS
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





Compositions of Transformations
Identify Symmetry
Identify and Perform Dilations
PROPERTIES OF CIRCLES
Properties of Tangents
Find Arc Measures
Apply Properties of Chords
CONTENT
PERFORMANCE TARGETS
(What Students should know)
(What Students should be able to do)
Students will be able to:

Rotate figures about a point

Rotate a figure using the coordinate rules

Use matrices to rotate a figure
DOUBLE REFLECTION
Students will use a graphing calculator to reflect a figure in
two lines in a plane
Students will be able to:

Perform combinations of two or more
transformations

Find the image of a glide reflection

Find image of a composition
INVESTIGATE DILATIONS
Students will use Geometer’s Sketchpad to construct
dilation of a figure
Students will be able to:

Identify line and rotational symmetries of a figure

Use drawing tools and matrices to draw dilations

Identify line of symmetry

Identify rotational symmetry
EXPLORE TANGENT SEGMENTS
Students will use Geometer’s Sketchpad to explore how the
lengths of tangent segments are related
Students will be able to:

Use properties of a tangent to a circle

Identify special segments and lines

Find lengths in circles in a coordinate plane
UNDERSTANDING CIRCLE VOCABULARY
Students will play a geometry vocabulary game
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Mathematics - Geometry
2010
KEY ELEMENTS
CONTENT
PERFORMANCE TARGETS
(What Students should know)
(What Students should be able to do)
Students will be able to:

Use angle measures to find arc measures

Use relationships of arcs and chords in a circle

Find measures of arcs

Identify congruent arcs

Use Inscribed Angles and Polygons


Other Angle Relationships in Circles
Segment Lengths in Circles

Write and Graph Equations of Circles
MEASURING LENGTH AND AREA
Areas of Triangles and
Parallelograms
 Areas of Trapezoids, Rhombuses,
and Kites

EXPLORE INSCRIBED ANGLES
Students will use Geometer’s Sketchpad to explore how
inscribed angles relate to central angles
Students will be able to:

Use inscribed angles of circles

Use circumscribed circles
Students will be able to:

Find the measures of angles inside or outside a
circle

Find segment lengths in circles

Find the angle and the arc measures

Find the angle measure inside a circle
DETERMINING EQUATIONS OF CIRCLES
Students will use Geometer’s Sketchpad to derive the
equation of a circle
Students will be able to:
Write equations of circles in the coordinate plane
DETERMINE PRECISION AND ACCURACY
Students will use Geometer’s Sketchpad to explore the
measuring distances in precision
Students will be able to:

Find areas of triangles and parallelograms

Find areas of other types of quadrilaterals
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Mathematics - Geometry
2010
KEY ELEMENTS

Perimeter and Area of Similar
Figures
CONTENT
PERFORMANCE TARGETS
(What Students should know)
(What Students should be able to do)
AREA OF TRAPEZOIDS AND KITES
Students will use graph paper to explore the use of a
parallelogram to find other areas
Students will be able to:

Find areas of other types of quadrilaterals

Use ratios to find areas of similar figures

Find the area of a quadrilateral

Find an area in the coordinate plane



Circumference and Arc Length
Areas of Circles and Sectors
Areas of Regular Polygons
EXPLORE CIRCUMFERENCE
Students will explore the ratio of circumference to
diameter and establish a formula for finding the
circumference of a circle when given diameter
Students will be able to:

Find arc lengths and other measures

Use the formula for circumference

Use arc length to find measures
AREAS OF CIRCLES AND SECTORS
Students will explore the area of circles and sectors
Students will be able to:

Find areas of circles and sectors of circles

Use the formula for area of a circle

Find the area of sectors
FINDING THE AREA OF REGULAR POLYGONS
Students will establish an equation for the area of a regular
polygon
Students will be able to:

Find areas of regular polygons inscribed in circles

Find angles measures in a regular polygon
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Mathematics - Geometry
2010
KEY ELEMENTS
CONTENT
PERFORMANCE TARGETS
(What Students should know)
(What Students should be able to do)


Geometric Probability
Find the perimeter and area of a regular polygon
INVESTIGATE GEOMETRIC PROBABILITY
Students explore how theoretical and experimental
probabilities compare
Students will be able to:

Use lengths and areas to find geometric
probabilities
SURFACE AREA AND VOLUME OF SOLIDS
 Explore Solids


Surface Area of Prism and Cylinders
Surface Area of Pyramids and Cones
INVESTIGATE SOLIDS
Students will investigate what solids can be made using
congruent regular polygons
Students will be able to:

Identify Solids

Identify and name polyhedra

Use euler’s theorem with platonic solids
INVESTIGATE SURFACE AREA
Students will explore how you can find the surface area of
a polyhedron
Students will be able to:

Find the surface areas of prisms and cylinders

Find the surface areas of pyramids and cones

Volume of Prisms and Cylinders
SURFACE AREAS OF PYRAMIDS AND CONES
Students will use Geometer’s Sketchpad to prove triangles
are congruent by Side-Side-Angle
Students will be able to:

Find the surface areas of pyramids and cones

Find the volume of prisms and cylinders

Find the area of a lateral face of a pyramid
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Mathematics - Geometry
2010
KEY ELEMENTS



Volume of Pyramids and Cones
Volume of Pyramids and Cones
Surface Area and Volume of Spheres
CONTENT
PERFORMANCE TARGETS
(What Students should know)
(What Students should be able to do)
VOLUME OF PRISMS AND CYLINDERS
Students will derive a formula for finding the volume of
Prisms and Cylinders
Students will be able to:

Find the volume of prisms and cylinders

Find the volume of pyramids and cones

Use volume of prism
INVESTIGATE TRIANGLES & CONGRUENCE
Students will explore the surface area of a pyramid
Students will be able to:

Find the volume of pyramids and cones

Find the surface area and volume of spheres

Find the volume of a solid

Use trigonometry to find the volume of a cone

Explore Similar Solids
Surface Area and Volume of Spheres
Students will play a game on surface area and volume of
spheres
Students will be able to:

Find the surface area and volume of spheres

Use properties of similar solids
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