Unit 1 – Coordinate Geometry (Parallel Lines)
Essential Questions:
1) How can you use coordinates and algebraic techniques to represent,
interpret and verify geometric relationships?
2) How do you use the ideas of direct/indirect proof and counterexamples
to verify valid conjectures and refute invalid conjectures?
Sections:
1.2
1.3
1.4
1.5
1.7
1.8
2.1
2.2
2.3
3.1
3.2
3.3
3.4
3.5
3.7
3.8
8.1
10.1
10.2
Points, Lines and Planes
Measuring Segments
Measuring Angles
Exploring Angle Pairs
Midpoint and Distance in the Coordinate Plane
Perimeter, Circumference, and Area
Patterns and Inductive Reasoning
Conditional Statements
Biconditionals and Definitions
Lines and Angles
Properties of Parallel Lines
Proving Lines Parallel
Parallel and Perpendicular Lines
Parallel Lines and Triangles
Equations of Lines in the Coordinate Plane
Slopes of Parallel and Perpendicular Lines
The Pythagorean Theorem and its Converse (wait for UNIT 2?)
Area of Parallelograms and Triangles (wait for area unit?)
Area of Trapezoids, Rhombuses, and Kites (only do trapezoids if it stays in
unit 1)
Unit 2 – Right Triangles
Essential Questions:
1) How can a change in one measurement of a 2 or 3 dimensional figure
effect other measurements such as perimeter, area, surface area or
volume of that figure?
2) How can you explain the relationship between congruence and similarity
in both 2 and 3 dimensional figures?
3) How do you use the ideas of direct/indirect proof and counterexamples
to verify valid conjectures and refute invalid conjectures?
Sections:
7.4
8.1
8.2
8.3
8.4
Similarity in Right Triangles
The Pythagorean Theorem
Special Right Triangles
Trigonometry
Angles of Elevation and Depression
Unit 3a – 2D Shapes
Essential Questions:
1) How can a change in one measurement of a 2 or 3 dimensional figure
effect other measurements such as perimeter, area, surface area or
volume of that figure?
2) How can we represent the probability of an event using geometric
properties of length or area?
3) How can you explain the relationship between congruence and similarity
in both 2 and 3 dimensional figures?
4) How can you use coordinates and algebraic techniques to represent,
interpret and verify geometric relationships?
5) How do you use the ideas of direct/indirect proof and counterexamples
to verify valid conjectures and refute invalid conjectures?
Sections: (Included on Midterm Examination)
4.1
4.2
4.3
4.4
4.5
4.6
4.7
5.1
5.2
5.3
5.4
5.5
5.6
5.7
Congruent Figures
Triangle Congruence by SSS and SAS
Triangle Congruence by ASA and AAS
Using Corresponding Parts of Congruent Triangles
Isosceles and Equilateral Triangles
Congruence and Right Triangles
Congruence in Overlapping Triangles
Midsegements of Triangles
Perpendicular and Angle Bisectors
Bisectors in Triangles
Medians and Altitudes
Indirect Proof
Inequalities in One Triangle
Inequalities in Two Triangles
Unit 3b – 2D Shapes
Essential Questions:
1) How can a change in one measurement of a 2 or 3 dimensional figure
effect other measurements such as perimeter, area, surface area or
volume of that figure?
2) How can we represent the probability of an event using geometric
properties of length or area?
3) How can you explain the relationship between congruence and similarity
in both 2 and 3 dimensional figures?
4) How can you use coordinates and algebraic techniques to represent,
interpret and verify geometric relationships?
5) How do you use the ideas of direct/indirect proof and counterexamples
to verify valid conjectures and refute invalid conjectures?
Sections: (Not Included on Midterm Examination)
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7.1
7.2
7.3
7.4
7.5
10.3
10.4
10.5
The Polygon-Angle Sum Theorem
Properties of Parallelograms
Proving that a Quadrilateral is a Parallelogram
Properties of Rhombuses, Rectangles, and Squares
Conditions for Rhombuses, Rectangles, and Squares
Trapezoids and Kites
Polygons in the Coordinate Plane
Applying Coordinate Geometry
Proofs Using Coordinate Geometry
Ratios and Proportions
Trigonometry and Area
Proving Triangles Similar
Similarity and Right Triangles
Proportions and Triangles
Areas of Regular Polygons
Perimeters and Areas of Similar Figures
Similar Polygons
Unit 4 – Circles
Essential Questions:
1) How can a change in one measurement of a 2 or 3 dimensional figure
effect other measurements such as perimeter, area, surface area or
volume of that figure?
2) How can we represent the probability of an event using geometric
properties of length or area?
3) How can you explain the relationship between congruence and similarity
in both 2 and 3 dimensional figures?
4) How do you use the ideas of direct/indirect proof and counterexamples
to verify valid conjectures and refute invalid conjectures?
Sections:
10.6
10.7
10.8
12.1
12.2
12.3
12.4
12.5
Circles and Arcs
Areas of Circles & Sectors
Geometric Probability
Tangent Lines
Chords and Arcs
Inscribed Angles
Angle Measures and Segment Lengths
Circles in the Coordinate Plane
Unit 5 – 3D Shapes
Essential Questions:
1) How can a change in one measurement of a 2 or 3 dimensional figure
effect other measurements such as perimeter, area, surface area or
volume of that figure?
2) How can we represent the probability of an event using geometric
properties of length or area?
3) How can you explain the relationship between congruence and similarity
in both 2 and 3 dimensional figures?
4) How can you use coordinates and algebraic techniques to represent,
interpret and verify geometric relationships?
5) How do you use the ideas of direct/indirect proof and counterexamples
to verify valid conjectures and refute invalid conjectures?
Sections:
11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.7
Space Figures and Cross Sections
Surface Areas of Prisms and Cylinders
Surface Areas of Pyramids and Cones
Volumes of Prisms and Cylinders
Volumes of Pyramids and Cones
Surface Areas and Volumes of Spheres
Perimeters and Areas of Similar Figures
Areas and Volumes of Similar Figures