Math - Geometry
Unit 1
- Definitions of angle, circle, point, distance, line segment, line, perpendicular and parallel lines
- Rotations, reflections, and translations of lines in the plane
- Transformations in terms of vertices, sides, angles, circles, lines, parallel lines, line segments, and perpendicular lines
- Rotations, reflections, and translations of polygons
- Sequence of transformations to carry one figure into another
- Angles and sums of angles created when parallel lines are cut by a transversal
- Congruence of two figures
- Criteria for triangle congruence
Unit 2
- Proving geometric theorems about lines, angles, and parallelograms
- Geometric constructions and bisections (including digital)
- Similarity
- Pythagorean Theorem and its converse
- Trigonometric ratios in right triangles
- Solving problems with trigonometric ratios in right triangles
- Trigonometry in general triangles
- Similarity of circles
Unit 3
- Elements of circles and relationships between them
- Constructing inscribed and circumscribed circles of a triangle
- Constructing tangents
- Arc lengths and areas of circle sectors
- Applying theorems about circles
- Deriving equations of parabola, ellipse, hyperbola, and center
- Proving theorems algebraically using coordinates
- Using coordinates to prove simple geometric theorems algebraically
Unit 4
- Proving slope criteria for parallel and perpendicular lines
- Finding the bisecting point on a line segment
- Computing perimeters and areas
- Explaining and using formulas for circumference, circle area, and volume of a cylinder, sphere, cone, and pyramid
- Cavalieri’s principle
- Shapes of two-dimensional slices of three-dimensional objects
- Geometric concepts in describing objects, modeling situations, and solving design problems
- Solving real world problems with geometric concepts and formulas