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Fall Semester Topics by Module:
Module 1
1.1 Segment Midpoints and Lengths
Constructing a Copy of a Line Segment
Midpoints and the Coordinate Plane
1.2 Angle Measures and Angle Bisectors
Constructing an Angle Bisector
1.3 Transformations
Rigid Motions using Coordinate Notation
Non-rigid Motions using Coordinate Notation
1.4 Reasoning and Proof
Module 2
2.1 Translations
Translations on a Coordinate Plane
2.2 Reflections
Reflecting Figures using Graph Paper
Drawing Reflections on a Coordinate Plane
Specifying Lines of Reflection
2.3 Rotations
Rotating using a Ruler and a Protractor
Drawing Rotations on a Coordinate Plane
2.4 Investigationg Symmetry
Module 3
3.1 Sequences of Transformations
Combining Rigid Transformations
Combining Non-Rigid Transformations
Predicting the Effect of Transformations
3.2 Proving figures are Congruent using Rigid Motions
Determining if Figures are Congruent
Finding a Sequence of Rigid Motions
Investigationg Congruent Angles and Segments
3.3 Corresponding Parts of Congruent Figures are Congruent
Corresponding Parts of Congruent Figures are Congruent
Applying the Properties of Congruence
Using the Corresponding Parts Theorem in Proof
4.1 Angles formed by intersecting lines
Proving the verticals angles theorem
Using Supplementary and Vertical Angles
4.2 Transversals and Parallel Lines
4.3 Proving Lines are Parallel
Proving Two lines are Parallel
Using Angles to Verify Lines are Parallel
4.4 Perpendicular Lines
Perpendicular Bisector Theorem
Converse Perpendicular Bisector Theorem
4.5 Equations of Parallel and Perpendicular Lines
Equations Of Perpendicular Lines
5.1 Exploring What Makes Triangles Congruent
Properties of Congruent Triangles
5.2 ASA Triangle Congruence
Prove Triangles Congruent using ASA
5.3 SAS Triangle Congruence
Prove Triangles Congruent using SAS
5.4 SSS Triangle Congruence
Prove Triangles Congruent using SSS
6.1 Justifying Constructions
Proving Angle Bisector and Perpendicular Bisector Constructions
6.2 AAS Triangle Congruence
6.3 HL Triangle Congruence
7.1 Interior and Exterior Angles
Proving Exterior Angle Theorem
7.2 Isosceles and Equilateral Triangles
Using Equilateral and Isosceles Triangles
7.3 Triangle Inequalities
Finding Possible Side Lengths in a Triangle
Ordering a Triangles Angles measures given its side lengths
Ordering a Triangles Side Lengths given its Angle Measures
8.1 Perpendicular Bisectors of Triangles
8.2 Angle Bisectors of Triangles
Constructing an Inscribed Angle
Using Properties of Angle Bisectors
8.3 Medians and Altitudes of Triangles
Intersection of Medians of a Triangle
Finding the Orthocenter of a Triangle
8.4 Midsegments of Triangles
9.1 Properties of Parallelograms
Proving Opposite Sides Congruent
Proving Opposite Angles Congruent
Proving Diagonals Bisect Each Other
Using Properties of Parallelograms
9.2 Conditions for Parallelograms
Verifying Figures as Parallelograms
9.3 Properties of Rectangles, Rhombuses, and Squares
Proving Diagonals of a Rectangle Congruent
Proving Diagonals of a Rhombus are Perpendicular
Using Properties of a Rhombus to find Measures
9.4 Conditions for Rectangles, Rhombuses, and Squares
Congruent Diagonals = Rectangles
Conditions for Special Parallelograms
9.5 Properties and Conditions for Kites and Trapezoids
Base Angles of Isosceles Trapezoids are Congruent
Calendar:
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10.1 Slope and Parallel Lines
Using Slopes to classify Quadrilaterals by sides
Using Slopes to Find Missing Vertices
10.2 Slopes and Perpendicular Lines
Using Slopes to Classify Figures by Right Angels
Using Slopes and Systems of Equations to Classify Equations
10.3 Coordinate Proof Using Distance with Segments and Triangles
Positioning a Triangle on the Coordinate Plane
Proving the Triangles Mid segment Theorem
Proving the Concurrency of Medians Theorem
Triangles on the Coordinate Plane
10.4 Coordinate Proof Using Distance with Quadrilaterals
Conditions for Special Parallelograms
Identifying Figures on a Coordinate Plane
10.5 Perimeter and Area on the Coordinate Plane
Area of Figures on the Coordinate Plane
Using Perimeter and Area in Problem Solving
11.1 Dilations
Applying Properties of Dilations
Finding the Center and Scale of a Dilation
11.2 Similarity and Transformations
Determining if Figures are Similar
11.3 Corresponding Parts of Similar Figures
Similar Figures using Transformation
11.4 AA Similarity of Triangles
Proving AA Triangle Similarity
12.1
Proving Triangle Proportionality Theorem
Applying Triangle Proportionality Theorem
Proving the Converse of the Triangle Proportionality Theorem
Applying the Converse of the Triangle Proportionality Theorem
12.2
Segments in a Two Dimensional Coordinate System
Constructing a Partition of a Segment
12.3
12.4
Finding Geometric Means of a Pair of Numbers
Proving the Geometric Means Theorems
Using the Geometric Means Theorems
Proving the Pythagorean Theorem via Similarity
13.1
Finding the Tangent of an Angle
Finding Angle Measure Using Tangent
13.2
Finding Sine and Cosine of an Angle
Finding Side Lengths using Sine and Cosine
Finding Angle Measures Using Sine and Cosine
13.3
Relationships in Special Triangles
Trig Ratios of Special Right Triangles
13.4
Solving a Right Triangle in the Coordinate Plane
14.1
14.2
15.1
Understanding Arcs and Arc Measure
Using the Inscribed Angle Theorem
Investigating Inscribed Angles on Diameters
15.2
Proving the Inscribed Quadrilateral Theorem
Applying the Inscribed Quadrilateral Theorem
Constructing an Inscribed Square
15.3
Proving the Tangent Radius Theorem
Constructing Tangents to a Circle
Proving the Circumscribed Angle Theorem
15.4
Applying the Chord Chord Product Theorem
Proving the Secant Secant Product Theorem
Applying the Secant Secant Product Theorem
Applying the Secant Tangent Product Theorem
15.5
Proving the Intersecting Chord Angle Measure Theorem
Applying the tangent secant interior angle measurement theorem
Applying the tangent secant exterior angle measurement theorem
Understanding angle relationships in circles
16.1
Applying the Circumference Formula
16.2
Applying the Formula for Arc Length
Arc Lengths in Concentric Circles
16.3
Formula for the Area of a Sector
Applying the Formula for the Area of a Sector
17.1
Writing the Equation of a Circle
Finding the Center and Radius of a Circle
18.1
18.2
18.3
18.4
19.1
Generating Three Dimensional Figures
19.2
Surface Area of a Composite Figure
19.3
Surface Area of a Composite Figure
19.4
Surface Area of a Composite Figure
21.1
Calculating Theoretical Probabilities
Using the Compliment of an Event
21.2
Finding a Probability using Permutations
Finding the number of Permutations with repetition
Finding a Probability using Permutations with Repetition
21.3
Finding a Probability using Combinations
Finding a Probability using Combinations and Addition