Common Core State Standards for Mathematics
Accelerated Geometry (V08) - Semester One
Domain: Congruence (GC)
Learning Standard: Experiment with transformations in the plane Test Questions
GCO0912.01 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. 1, 2
GCO0912.02 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). 3, 4, 5
GCO0912.03 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. 6, 7
GCO0912.04 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. 8, 9
GCO0912.05 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. 10, 11
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. 12, 13
GCO0912.07 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. 14, 15
GCO0912.08 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. 16, 17, 18, 19
Learning Standard: Prove geometric theorems Test Questions
GCO0912.09 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. 22, 23
FR5
GCO0912.10 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. 24
FR3
Learning Standard: Make geometric constructions Test Questions
GCO0912.12 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. FR1, 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.
25, 26
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. 27
FR4
GSRT0912.03 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. 28, 29, 30
Learning Standard: Prove theorems involving similarity Test Questions
GSRT0912.04 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. 31, 32
GSRT0912.05 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. 20, 21, 33, 34, 35, 36, 37, 38, 39
Learning Standard: 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. 40
Domain: Expressing Geometric Properties with Equations (GGPE)
Learning Standard: Use coordinates to prove simple geometric theorems algebraically Test Questions
GGPE0912.05 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 41, 42, 43
GGPE0912.06 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. 44, 45

 

Total: 45 points
Free Response: 20 points
Overall: 65 points

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