Introduction to Coordinate Geometry
The students will use multiple representations of undefined terms on a coordinate plane to solve problems.
Coordinate Geometry: Parallel and Perpendicular Lines
Given characteristics of two lines, such as slopes and equations, the student will determine whether the lines are parallel, perpendicular, or neither.
Coordinate Geometry: Special Segments
The student will derive and use the slope and midpoint formulas to verify geometric relationship that include parallelism and perpendicularity of lines. Then, the student will determine an equation of a line parallel or perpendicular to a given line.
Coordinate Geometry: Length and Distance
Given coordinates of points, the student will use the distance formula to solve problems involving length and distance.
Coordinate Geometry: Slope
Given coordinate points, the student will use slope formulas to solve problems.
Describing and Drawing Cross Sections
Given a verbal and/or pictorial description of the intersection of a plane with various three-dimensional geometric figures, the student will describe and/or draw the intersection.
Determining Area: Composite Figures
Given information about composite fiugres, the student will determine the area of composite 2-dimensional figures comprised of a combination of triangles and parallelograms using appropriate units of measure.
Determining Arc Length
Given a problem situation involving sectors of circles, the student will use proportional reasoning to solve the problem.
Using The Pythagorean Theorem
The student will use triangle relationships to prove the Pythagorean Theorem and solve problems.
Applying Geometric Probability
The student will find the area of polygons and circles. Then, the student will use probability to solve real-world problems.
Determining the Surface Area of Cones and Cylinders
Given a problem involving cones or cylinders, the student will find the surface area using appropriate units of measure.
Determining the Volume of Cones and Cylinders
Given a problem involving cones or cylinders, the student will find the volume using appropriate units of measure.
Determining the Surface Area and Volume of Spheres
Given a problem involving spheres, the student will find the surface area and volume.
Determining the Surface Area and Volume of Composite Figures
Given a problem involving composite figures made from prisms, pyramids, spheres, cones, and/or cylinders, the student will find the surface area and volume of the composite figure.
Making Conjectures about Parallel and Perpendicular Lines
The student will verify theorems about angles formed by parallel lines cut by a transversal and apply these relationships to solve problems.
Making and Verifying Conjectures About Triangles
Given examples of triangles and their component parts, the student will use explorations and concrete models to verify and apply the Triangle Inequality theorem and find the sum of interior angles.
Determining the Surface Area of Prisms and Pyramids
Given a problem involving prisms or pyramids, the student will find the surface area using appropriate units of measure.
Determining the Volume of Prisms and Pyramids
Given a problem involving prisms or pyramids, the student will find the volume using appropriate units of measure.
Making Conjectures About Congruence Transformations
Given geometric figures on the coordinate plane, the student will apply the definition of congruence, in terms of rigid transformations, to identify congruent figures. The student will also identify and distinguish between reflectional and rotational symmetry in a plane figure.
Making Conjectures About Quadrilaterals
Given examples of quadrilaterals and their component parts, the student will use explorations and concrete models to prove a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite sides, opposite angles, or diagonals.