Geometry Station Activities for Common Core Standards

Grades 9-12.

For your Common Core curriculum.

Students learn to apply geometry concepts, employ problem-solving strategies, communicate with one another, and reason through to the answers while working together. Multiple sets of activities focus on Congruence, Similarity, Right Triangles, Trigonometry, Circles, and Expressing Geometric Properties with Equations. Each set consists of 4 different stations (10-15 minutes each) where students work in small groups on multiple sets of activities, moving from station to station once their activities are complete. A debrief discussion follows the station activities. Uses readily available materials and manipulatives (not included). Includes teacher support with discussion guides, answer keys, and material lists. 252 reproducible pages.

CCSS Product Alignment

HSG.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software, describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

HSG.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

HSG.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

HSG.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

HSG.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.

HSG.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

HSG.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

HSG.CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent, when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent, points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

HSG.CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°, base angles of isosceles triangles are congruent, the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length, the medians of a triangle meet at a point.

HSG.CO.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

HSG.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment, copying an angle, bisecting a segment, bisecting an angle, constructing perpendicular lines, including the perpendicular bisector of a line segment, and constructing a line parallel to a given line through a point not on the line.

HSG.CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

HSG.SRT.1a A 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.

HSG.SRT.1b The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

HSG.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 the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

HSG.SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely, the Pythagorean Theorem proved using triangle similarity.

HSG.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

HSG.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

HSG.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles.

HSG.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

HSG.C.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles, inscribed angles on a diameter are right angles, the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

HSG.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

HSG.C.4 (+) Construct a tangent line from a point outside a given circle to the circle.

HSG.C.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality, derive the formula for the area of a sector.