Unit 1: Building Blocks of Geometry 1. Introduction to foundational vocabulary and extending the understanding of undefined terms 2. Use the Pythagorean Theorem to derive the distance formula 3. Apply and use the midpoint formula
Unit 2: Parallel Lines and Transversals 1. Define and classify special angle pairs 2. Apply and use parallel line and perpendicular line theorems 3. Use construction tools to construct parallel and perpendicular lines 4. Use slope criteria to write equations of parallel and perpendicular lines 5. Use geometric tools to complete basic constructions, using the definitions to validate those constructions 6. Use construction tools to construct parallel lines
Unit 3: Transformations 1. Explore transformations on the coordinate plane to define congruence and similarity
Unit 4: Triangles 1. Classify triangles using properties 2. Solve problems using congruence of triangles on the coordinate plane 3. Complete proofs about relationships in triangles 4. Solve for and construct special segments of a triangle 5. Identify and prove points of concurrency 6. Complete proofs and solve problems of triangle theorems 7. Apply triangle theorems to solve problems 8. Prove and solve problems using triangle inequities/hinge theorem
Unit 5: Quadrilaterals 1. Classify polygons and use the interior and exterior angle properties 2. Define, prove, and apply properties of parallelograms (rectangles, rhombi, squares) 3. Apply properties of trapezoids and kites to solve problems 4. Use coordinates to prove/disprove properties of quadrilaterals on a graph 5. Apply transformations that will carry a quadrilateral onto itself and construct a square and a hexagon in a circle
Unit 6: Similarity 1. Identify the scale factor and center of a dilation 2. Partition a segment into a given ratio 3. Use triangle similarity to prove theorems about triangles and solve for missing lengths/angles 4. Complete and apply proofs about triangle relationships
Unit 7: Right Triangles 1. Apply the properties of special right triangles to solve problems including the geometric mean theorem 2. Derive Pythagorean theorem using triangle similarity 3. Solve for sides and angles of a triangle using trigonometry 4. Model and solve problems using angles of elevation and depression
Unit 8: Area and perimeter of two dimensional shapes 1. Calculate the area and perimeter of triangles, quadrilaterals, circles, and composite figures 2. Derive and calculate formulas for area of trapezoid, kite, rhombus, and regular polygons 3. Using ratios, compare and contrast areas and perimeters of similar figures 4. Derive and calculate formulas for the areas of a sector and a segment of a circle 5. Complete proofs on a coordinate plane for areas and perimeter of regular and irregular polygons 6. Model and solve problems using population density
Unit 9: Three Dimensional Figures 1. Derive formula and solve for surface and lateral area and volume of three dimensional shapes including real life applications 2. Explore rotations of two dimensional shapes and determine the cross section of three dimensional shapes 3. Model a situation involving density 4. Identify the shapes of two-dimensional cross-sections within three dimensional objects
Unit 10: Circles 1. Explore and apply characteristics of circles 2. Complete the square to find the center and radius of a circle and derive the equation using the Pythagorean Theorem 3. Complete proofs using coordinates and/or algebra to prove/disprove properties of circles 4. Write equations of circles that are transformed