Common Core State Standards for Mathematics
Sheltered Geometry (V01) Semester One
Domain: Congruence (GCO)
Learning Standard: Experiment with transformations in the plane. Test Questions
GCO09-12.01 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. MC: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Learning Standard: Understand congruence in terms of rigid motions. Test Questions
GCO09-12.08 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. MC: 24, 27
Learning Standard: Prove geometric theorems. Test Questions
GCO09-12.09 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. MC: 12, 13, 14, 15 FR: 2, 3
GCO09-12.10 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. MC: 16, 17, 18, 19, 28, 29, 30, 31, 32, 33 FR: 4
Domain: Expressing Geometric Properties With Equations (GGPE)
Learning Standard: Use coordinates to prove simple geometric theorems algebraically. Test Questions
GGPE09-12.05 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). MC: 20, 34
GGPE09-12.06 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. MC: 11
GGPE09-12.07 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. FR: 1
Domain: Similarity, Right Triangles, & Trigonometry (GSRT)
Learning Standard: Understand similarity in terms of similarity transformations. Test Questions
GSRT09-12.02 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. MC: 35
GSRT09-12.03 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. MC: 38
Learning Standards: Prove theorems involving similarity. Test Questions
GSRT09-12.04 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. MC: 36
GSRT09-12.05 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. MC: 21, 22, 23, 25, 26, 37, 39, 40, 41
Domain: Conditional Probability and The Rules of Probability (SCP)
Learning Standard: Understand independence and conditional probability and use them to interpret data. Test Questions
SCP09-12.04 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. MC: 43, 44, 45
Learning Standard: Use the rules of probability to compute probabilities of compound events in a uniform probability model. Test Questions
SCP09-12.08 Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. MC: 42

Multiple Choice: 45 points
Free Response: 10 points
Overall: 55 points

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