Common Core State Standards for Mathematics
Sheltered Geometry (V01) Semester Two
Domain: Congruence (GCO)
Learning Standard: Experiment with transformations in the plane. Test Questions
GCO0912.03 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. 19
GCO0912.05 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, i.e., graph paper, tracing paper, or geometry software, Specify a sequence of transformations that will carry a given figure onto another. 20, 21
Learning Standard: Understand congruence in terms of rigid motions. Test Questions
GCO0912.06 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. 23, 24
Learning Standard: Prove geometric theorems. Test Questions
GCO0912.11 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. 11, 12, 13, 14, 15, 16
FR2
Domain: Similarity, Right Triangles, & Trigonometry (GSRT)
Learning Standard: Understand similarity in terms of similarity transformations. Test Questions

GSRT0912.01 Verify experimentally the properties of dilations given by a center and a scale factor:

• 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.
• The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
22, 25
GSRT0912.02 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. 28, 29
Learning Standards: Prove theorems involving similarity. Test Questions
GSRT0912.05 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. 10, 17, 18
Learning Standards: Define trigonometric ratios and solve problems involving right triangles. Test Questions
GSRT0912.06 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. 1, 2, 3, 4
GSRT0912.08 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. 5, 6, 7, 8, 9
FR1
Domain: Circles (GC: GCA or GCB)
Learning Standard: Understand and apply theorems about circles. Test Questions
GCA0912.02 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. 31, 32, 34, 35, 38, 39, 40, 41
GCA0912.03 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. 36, 37
Learning Standard: Find arc lengths and areas of sectors of circles. Test Questions
GCB0912.05 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. 30, 33
Domain: Expressing Geometric Properties With Equations (GGPE)
Learning Standard: Translate between the geometric description and the equation for a conic section. Test Questions
GGPE0912.01 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. 42
Learning Standard: Use coordinates to prove simple geometric theorems algebraically. Test Questions
GGPE0912.07 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. 26, 27
Domain: Geometric Measurement and Dimension (GGMD)
Learning Standard: Explain volume formulas and use them to solve problems. Test Questions
GGMD0912.01 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. FR3
GGMD0912.03 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. 43, 44, 45
FR 4

Multiple Choice: 45 points
Free Response: 13 points
Overall: 58 points

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