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10th grade
Content
- Prove polynomial identities
- Experiment with transformations in the plane
- Represent transformations in the plane
- Describe rotations and reflections
- Develop definitions of rotations, reflections and translations
- Experiment with transformations in the plane
- Understand congruence in terms of rigid motions
- Use rigid motions to show that two polygons are congruent
- Understand triangle congruence
- Prove geometric theorems
- Prove geometric theorems about triangles
- Prove geometric theorems about parallelograms
- Make geometric constructions
- Make larger geometric constructions
- Understand similarity in terms of similarity transformations
- The connection by the scale factor and the dilation
- Use similarity transformations to show that to figures are similar
- Understand the AA similarity rule
- Prove theorems involving similarity
- Use congruence and similarity to solve problems
- Understand the connection between the sides and the angles of a triangle
- The relationship between sine and cosine
- Understand trigonometric ratios
- Prove that all circles are similar
- Understand Thales's theorem
- Understand circle of Apollonius
- Find arc lengths and areas of sectors of circles
- The equation of a circle
- The equation of a parabola
- Derive the equation of a parabola
- Derive the equation of a ellipse and a hyperbola
- Use coordinates to prove a figure is a rectangle
- Use coordinates to prove simple geometric theorems algebraically
- Explain volume formulas and use them to solve problems
- Use volume formulas to solve problems
- Use formulas for cylinders, pyramids, cones, and spheres to solve problems
- From 3D to 2D
- Use geometric shapes to describe objects
- Volumetric mass density
- Geometry and optimization
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