Next Generation Learning Standards
1.1.1: Experiment with transformations in the plane.
GEO-G.CO.1: Know precise definitions of angle, circle, perpendicular lines, parallel lines, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc as these exist within a plane.
Circles
Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Inscribed Angles
Parallel, Intersecting, and Skew Lines
GEO-G.CO.2: Represent transformations as geometric functions that take points in the plane as inputs and give points as outputs. Compare transformations that preserve distance and angle measure to those that do not.
Dilations
Reflections
Rotations, Reflections, and Translations
Translations
GEO-G.CO.3: Given a regular or irregular polygon, describe the rotations and reflections (symmetries) that map the polygon onto itself.
Dilations
Reflections
Rotations, Reflections, and Translations
Similar Figures
GEO-G.CO.4: Develop definitions of rotations, reflections, and translations in terms of points, angles, circles, perpendicular lines, parallel lines, and line segments.
Circles
Dilations
Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations
GEO-G.CO.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure. Specify a sequence of transformations that will carry a given figure onto another.
Dilations
Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations
1.1.2: Understand congruence in terms of rigid motions.
GEO-G.CO.6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure. Given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
Absolute Value with Linear Functions
Circles
Dilations
Holiday Snowflake Designer
Proving Triangles Congruent
Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations
GEO-G.CO.8: Explain how the criteria for triangle congruence (ASA, SAS, SSS, AAS and HL (Hypotenuse Leg)) follow from the definition of congruence in terms of rigid motions.
1.1.3: Prove geometric theorems
GEO-G.CO.9: Prove and apply theorems about lines and angles.
GEO-G.CO.10: Prove and apply theorems about triangles.
Isosceles and Equilateral Triangles
Polygon Angle Sum
Proving Triangles Congruent
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Triangle Angle Sum
Triangle Inequalities
GEO-G.CO.11: Prove and apply theorems about parallelograms.
Parallelogram Conditions
Special Parallelograms
1.1.4: Make geometric constructions.
GEO-G.CO.12: Make, justify, and apply formal geometric constructions.
Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors
GEO-G.CO.13: Make and justify the constructions for inscribing an equilateral triangle, a square and a regular hexagon in a circle.
Concurrent Lines, Medians, and Altitudes
Inscribed Angles
1.2.1: Understand similarity in terms of similarity transformations.
GEO-G.SRT.1: Verify experimentally the properties of dilations given by a center and a scale factor.
GEO-G.SRT.1.a: Verify experimentally that dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
GEO-G.SRT.1.b: Verify experimentally that the dilation of a line segment is longer or shorter in the ratio given by the scale factor.
GEO-G.SRT.2: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar. Explain using similarity transformations that similar triangles have equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
Circles
Dilations
Similar Figures
Similarity in Right Triangles
GEO-G.SRT.3: Use the properties of similarity transformations to establish the AA~, SSS~, and SAS~ criterion for two triangles to be similar.
1.2.2: Prove theorems involving similarity.
GEO-G.SRT.4: Prove and apply similarity theorems about triangles.
Congruence in Right Triangles
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Similar Figures
GEO-G.SRT.5: Use congruence and similarity criteria for triangles to:
Chords and Arcs
Congruence in Right Triangles
Constructing Congruent Segments and Angles
Dilations
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures
Similarity in Right Triangles
GEO-G.SRT.5.a: Solve problems algebraically and geometrically.
Chords and Arcs
Congruence in Right Triangles
Constructing Congruent Segments and Angles
Dilations
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures
Similarity in Right Triangles
GEO-G.SRT.5.b: Prove relationships in geometric figures.
Chords and Arcs
Congruence in Right Triangles
Constructing Congruent Segments and Angles
Dilations
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures
Similarity in Right Triangles
1.2.3: Define trigonometric ratios and solve problems involving right triangles.
GEO-G.SRT.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of sine, cosine and tangent ratios for acute angles.
Sine, Cosine, and Tangent Ratios
GEO-G.SRT.8: Use sine, cosine, tangent, the Pythagorean Theorem and properties of special right triangles to solve right triangles in applied problems.
Cosine Function
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function
1.3.1: Understand and apply theorems about circles.
GEO-G.C.2a: Identify, describe and apply relationships between the angles and their intercepted arcs of a circle.
Chords and Arcs
Circumference and Area of Circles
Inscribed Angles
GEO-G.C.2b: Identify, describe and apply relationships among radii, chords, tangents, and secants of a circle.
Chords and Arcs
Circumference and Area of Circles
Inscribed Angles
1.3.2: Find arc lengths and area of sectors of circles.
GEO-G.C.5: Using proportionality, find one of the following given two others: the central angle, arc length, radius or area of sector.
1.4.1: Translate between the geometric description and the equation of a conic section.
GEO-G.GPE.1a: Derive the equation of a circle of given center and radius using the Pythagorean Theorem. Find the center and radius of a circle, given the equation of the circle.
Circles
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
GEO-G.GPE.1b: Graph circles given their equations.
1.4.2: Use coordinates to prove simple geometric theorems algebraically.
GEO-G.GPE.5: On the coordinate plane:
GEO-G.GPE.5.b: Determine if lines are parallel, perpendicular, or neither, based on their slopes; and
Cat and Mouse (Modeling with Linear Systems)
GEO-G.GPE.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.
1.5.1: Explain volume formulas and use them to solve problems.
GEO-G.GMD.1: Provide informal arguments for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.
Circumference and Area of Circles
Prisms and Cylinders
Pyramids and Cones
GEO-G.GMD.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Prisms and Cylinders
Pyramids and Cones
Correlation last revised: 12/9/2022