**Honors Geometry Topics**

*All topics listed below are presented to the students in a way that is consistent with the vision of the NCTM (National Council of Teachers of Mathematics)***1. Tools of Geometry**

**Patterns and Inductive Reasoning****Points, Lines, and Planes****Segments, Rays, Parallel Lines,and Planes****Measuring Segments****Measuring Angles****Basic Constructions****The Coordinate Plane****Perimeter, Circumference, and Area**

**2. Reasoning and Proof**

**Conditional Statements****Biconditionals and Definitions****Deductive Reasoning****Reasoning inAlgebra****Proving Angles Congruent**

**3. Parallel and Perpendicular Lines**

**Properties of Parallel Lines****Proving Lines Parallel****Parallel and Perpendicular Lines****Parallel Lines and the Triangle Angle-Sum Theorem****The Polygon Angle-Sum Theorems****Lines in the coordinate Plane****Slopes of Parallel and Perpendicular Lines****Constructing Parallel and Perpendicular Lines**

**4. Congruent Triangles**

**Congruent Figures****Triangle Congruence by SSS and SAS****Triangle Congruence by ASA and AAS****Using Congruent Triangles CPCTC****Isosceles and Equilateral Triangles****Congruence in Right Triangles****Using Corresponding Parts of Congruent Triangles.**

**5. Relationships Within Triangles**

**Midsegments of Triangles****Bisectors in Triangles****Congruent Lines, Medians, and Altitudes****Inverses, Contrpositives, and Indirect Reasoning****Inequalities in Triangles**

**6. Quadrilaterals**

**Classifying Quadrilaterals****Properties of Parallelograms****Proving that a Quadrilateral is a Parallelogram****Special Parallelograms****Trapezoids and Kites****Coordinate Geometry**

**7. Similarity**

**Ratios and Proportions****Similar Polygons****Proving Triangles Similar****Similarity in Right Triangles****Proportions in Triangles**

**8. Right Triangles and Trigonometry**

**The Pythagorean Theorem and its Converse****Special Right Triangles****The Tangent Ratio****Sine and Cosine Ratio****Angles of Elevation and Depression**

**9. Transformations**

**Translations****Reflections****Rotations****Symmetry****Dilations****Compositions of Reflections**

*10. Area***Areas of Parallelograms and Triangles****Areas of Trapezoids, Rhombuses, and Kites****Areas of Regular Polygons****Perimeters and Areas of Similar Figures****Circles and Arcs****Areas of Circles and Sectors****Geometric Probability**

*11. Surface Area and Volume***Space Figures and Cross Sections****Surface Areas of Prisms and Cylinders****Surface Areas of Pyramids and Cones****Volumes of Prisms and and Cylinders****Volumes of Pyramids and Cones****Surface Areas and Volumes of Spheres****Areas and Volumes of Similar Solids**

*12. Circles***Tangent Lines****Chords and Arcs****Inscribed Angles****Angle Measures and Segment Lengths****Circles in the Coordinate Plane****Locus: A Set Of Points**