PreAP Geometry Year at a Glance

• Course Overview:

Geometry is a foundational mathematics course that introduces students to the language of geometry, mathematical reasoning, and problem-solving techniques. At DeBakey High School for Health Professions, this course is designed to build deep conceptual understanding and prepare students for higher-level math courses such as Algebra 2, and AP coursework.

🟦 Chapter 1: Tools of Geometry

1-1 Points, Lines, and Planes

1-2 Measuring Segments

1-3 Measuring Angles

1-4 Exploring Angle Pairs

1-5 Basic Constructions

🟦 Chapter 2: Reasoning and Proof

2-1 Patterns and Conjectures

2-2 Conditional Statements

2-3 Biconditionals and Definitions

2-4 Deductive Reasoning

2-5 Reasoning in Algebra and Geometry

2-6 Proving Angles Congruent

🟦 Chapter 3: Parallel and Perpendicular Lines

3-1 Lines and Angles

3-2 Properties of Parallel Lines

3-3 Proving Lines Parallel

3-4 Parallel and Perpendicular Lines

3-5 Parallel Lines and Triangles

3-6 Constructing Parallel and Perpendicular Lines

3-7 Equations of Lines in the Coordinate Plane

3-8 Slopes of Parallel and Perpendicular Lines

3-9 Comparing Spherical and Euclidean Geometry

🟦 Chapter 4: Congruent Triangles

4-1 Congruent Figures

4-2 Triangle Congruence by SSS and SAS

4-3 Triangle Congruence by ASA and AAS

4-4 Using Corresponding Parts of Congruent Triangles

4-5 Isosceles and Equilateral Triangles

4-6 Congruence in Right Triangles

4-7 Congruence in Overlapping Triangles

🟦 Chapter 5: Relationships Within Triangles

5-1 Midpoint and Distance in the Coordinate Plane

5-2 Midsegments of Triangles

5-3 Perpendicular and Angle Bisectors

5-4 Bisectors in Triangles

5-5 Medians and Altitudes

5-6 Indirect Proof

5-7 Inequalities in One Triangle

5-8 Inequalities in Two Triangles

🟦 Chapter 6: Polygons and Quadrilaterals

6-1 The Polygon Angle-Sum Theorems

6-2 Properties of Parallelograms

6-3 Proving That a Quadrilateral Is a Parallelogram

6-4 Properties of Rhombuses, Rectangles, and Squares

6-5 Conditions for Rhombuses, Rectangles, and Squares

6-6 Trapezoids and Kites

🟦 Chapter 7: Coordinate Geometry

7-1 Polygons in the Coordinate Plane

7-2 Applying Coordinate Geometry

7-3 Proofs Using Coordinate Geometry

🟦 Chapter 8: Transformational Geometry

8-1 Translations

8-2 Reflections

8-3 Rotations

8-4 Symmetry

8-5 Compositions of Rigid Transformations

8-6 Congruence Transformations

8-7 Dilations

8-8 Other Non-Rigid Transformations

🟦 Chapter 9: Similarity

9-1 Similar Polygons

9-2 Similarity Transformations

9-3 Proving Triangles Similar

9-4 Similarity in Right Triangles

9-5 Proportions in Triangles

🟦 Chapter 10: Right Triangles and Trigonometry

10-1 The Pythagorean Theorem and Its Converse

10-2 Special Right Triangles

10-3 Trigonometry

10-4 Angles of Elevation and Depression

🟦 Chapter 11: Circle Measurement

11-1 Circles and Arcs

11-2 Radian Measure

11-3 Areas of Circles and Sectors

11-4 Circles in the Coordinate Plane

🟦 Chapter 12: Theorems About Circles

12-1 Tangent Lines

12-2 Chords and Arcs

12-3 Inscribed Angles

12-4 Angle Measures and Segment Lengths

🟦 Chapter 13: Area

13-1 Areas of Parallelograms and Triangles

13-2 Areas of Trapezoids, Rhombuses, and Kites

13-3 Areas of Regular Polygons

13-4 Perimeters and Areas of Similar Figures

13-5 Trigonometry and Area

🟦 Chapter 14: Surface Area and Volume

14-1 3-D Figures and Cross Sections

14-2 Surface Areas of Prisms and Cylinders

14-3 Surface Areas of Pyramids and Cones

14-4 Volumes of Prisms and Cylinders

14-5 Volumes of Pyramids and Cones

14-6 Surface Areas and Volumes of Spheres

14-7 Surface Areas and Volumes of Related Solids

🟦 Chapter 15: Probability

15-1 Experimental and Theoretical Probability

15-2 Geometric Probability

15-3 Permutations and Combinations

15-4 Compound Probability

15-5 Conditional Probability with Freq-Tables

15-6 Conditional Probability Formulas