Geometry Lessons Using
Advanced Technology
Geometry Scope and Sequence
| Unit Title | Students will be able to: | Activities |
|---|---|---|
| Unit 1 Geometry Foundations & Algebraic Connections | Derive and use the distance, slope, and midpoint formulas in one- and two-dimensional coordinate systems. Use distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines. Determine an equation of a line parallel or perpendicular to a given line that passes through a given point. Distinguish between undefined terms, definitions, postulates, conjectures, and theorems. | Exploring Linear Functions Points, Lines, and Angles—Always, Sometimes, Never Slopes of Parallel and Perpendicular Lines Inquiry Understanding the Distance Formula |
| Unit 2 Conditional Statements | Identify the converse, inverse, and contrapositive of a conditional statement, and determine its validity. Recognize a biconditional statement as a true conditional statement with a true converse. Use counterexamples to verify that a conjecture is false. | Conditional Statements Conditionals in Mathematics On One Condition |
| Unit 3 Parallel and Perpendicular Lines | Use a compass and straightedge to construct segments, congruent angles, segment and angle bisectors, perpendicular lines and perpendicular bisectors, and lines parallel to a given line through a point not on the line; use the constructions to make conjectures about geometric relationships. Analyze patterns of angle measures to make conjectures about angles formed by intersecting lines and parallel lines cut by a transversal. Verify theorems and solve problems about angles formed by parallel lines and transversals and use these relationships to solve problems. Prove equidistance between the endpoints of a segment and points on its perpendicular bisector and use this relationship to solve problems. Derive formulas for the measures of interior and exterior angles of polygons. Explore relationships created by special segments of triangles and diagonals of quadrilaterals. | Basic Geometric Constructions Angles in a Triangle Angles and Lines at a Point Angles of Polygons Transversals |
| Unit 4 Triangles | Verify the Triangle Inequality Theorem and apply it to solve problems. Determine the conditions required for triangle congruence. Prove two triangles are congruent by applying the triangle congruence conditions. Identify congruent figures and their corresponding sides and angles. Prove segments or angles congruent by applying the corresponding parts theorem. Verify theorems about relationships in triangles, including the sum of interior angles, base angles of isosceles triangles, midsegments, and medians, and use these relationships to solve problems. | Triangle Sides and Angles Interior and Exterior Angles of a Triangle Congruent or Not |
| Unit 5 Transformations | Describe and perform transformations of figures in a plane using coordinate notation. Determine the image or pre-image of a two-dimensional figure under a composition of transformations. Identify the sequence of transformations that will carry a given pre-image onto an image. Apply the definition of congruence, in terms of rigid transformations, to identify congruent figures and their corresponding parts. Distinguish between reflectional and rotational symmetry in a plane figure. | Reflections Rotations Scale Factor Transformations |
| Unit 6 Similarity | Apply the definition of similarity in terms of dilation to identify similar figures and their proportional sides and the congruent corresponding angles. Prove the Angle-Angle Theorem and the Triangle Proportionality Theorem and apply them to solve problems. Identify and apply the relationships that exist when an altitude is drawn to the hypotenuse of a right triangle, including the geometric mean, to solve problems. | Midsegments of Triangles Sidesplitter Theorem Geometric Mean |
| Unit 7 Right Triangles | Explore proofs of the Pythagorean Theorem. Use Pythagorean triples, the Pythagorean Theorem, and the converse of Pythagorean Theorem to solve problems involving the measures of the sides and angles of a right triangle. Apply the relationships in special right triangles (30-60-90 and 45-45-90) to solve problems. Determine the measures of the sides and angles of a right triangle by applying the trigonometric ratios (sine, cosine, tangent). | Pythagorean Theorem Special Right Triangles Trig Ratios |
| Unit 8 Quadrilaterals | Prove a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite sides, opposite angles, or diagonals. Apply theorems about quadrilaterals to solve problems. | Parallelogram Properties Interactive Worksheet Properties of Parallelograms Rhombi, Kites, and Trapezoids Quadrilateral Property Sort Working with Quadrilaterals Circuit Training |
| Unit 9 Circles | Investigate patterns in special segments and angle measures of circles.
Apply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to solve problems. Apply the proportional relationship between the measure of an arc length and the circumference of a circle to solve problems. Describe the radian measure of an angle as the ratio of the length of an arc intercepted by a central angle and the radius of the circle. Relate the equation of a circle to the distance formula. Determine the equation for the graph of a circle. | Circle Vocabulary Activity Angles and Arcs Circle Product Theorems Putting It All Together (Circles) |
| Unit 10 Area | Derive and apply the formulas for the area of regular polygons to solve problems using appropriate units of measure. Determine the area of composite two-dimensional figures comprised of a combination of polygons and/or sectors of circles to solve problems, using appropriate units of measure. | Area of a Regular Polygon Boardroom Table Arcs, Sector Areas, and Segment Areas Grudgeball |
| Unit 11 Space Figures | Identify the shapes of two-dimensional cross-sections of prisms, pyramids, cylinders, cones, and spheres. Identify three-dimensional objects generated by rotations of two-dimensional shapes. Derive and apply the formulas for the total and lateral surface area of three-dimensional prisms, pyramids, cones, cylinders, spheres, and composite figures to solve problems, using appropriate units of measure. Derive and apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems, using appropriate units of measure. Determine how changes in the linear dimensions of a shape affect its perimeter, area, or volume, including proportional and non-proportional dimensional change. | Surface Area of a Cylinder Family Tent Quandary Volume of Solids Chain Activity Wax Museum Making a Splash |
| Unit 12 Probability | Develop strategies to use permutations and combinations to solve problems. Determine probabilities based on the area to solve contextual problems. Identify whether two events are independent and compute the probability of two events occurring together with or without replacement. Apply conditional probability to solve contextual problems. Apply independence in contextual problems. | Permutations and Combinations Formula Discovery Coin Toss Games Permutations and Combinations Calculator Activity |