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10th grade
Polynomials
Prove polynomial identities
Planar Figures
Experiment with transformations in the plane
Transformations in the Coordinate Plane
Represent transformations in the plane
Describe rotations and reflections
Develop definitions of rotations, reflections and translations
Congruence
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
Similarity
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
Circles
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
Parabolas and Ellipses
The equation of a parabola
Derive the equation of a parabola
Derive the equation of a ellipse and a hyperbola
The Coordinate Plane
Use coordinates to prove a figure is a rectangle
Use coordinates to prove simple geometric theorems algebraically
Volume
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
3D to 2D
From 3D to 2D
Modeling with Geometry
Use geometric shapes to describe objects
Volumetric mass density
Geometry and optimization