# Geometry Learning Targets

Math, Geometry

ALT 1 - Single Variable Data

I can display and describe single variable data and identify sampling bias.

**AST 1.1 - Graphically Rep. Single Variable Data** : Graphically represent single variable data using dot plots, histograms, and box plot.

**AST 1.2 - Compute Measures of Center** : Compute measures of center including mean and median.

**AST 1.3 - Measures of Spread** : Compute or find with a calculator measures of spread including standard deviation, range, and interquartile range.

**AST 1.4 - Compute Measures of Position** : Compute measures of position including minimum, maximum, first quartile, third quartile, and percentiles.

**AST 1.5 - Analyze and Compare Data Sets** : Analyze and compare data sets using measures of center, spread and position.

**AST 1.6 - Determine Type of Sample** : Determine the type of sampling used and identify any potential bias.

ALT 2 - Foundations of Geometry

I can demonstrate my understanding of the foundations of geometry.

**AST 2.1 - Consistently Translate** : Consistently translate between vocabulary, symbols and or a diagram to communicate.

**AST 2.2 - Correctly Identify Vocabulary** : Correctly identify in words and symbols the following vocabulary including but not limited to: undefined terms (point, line, plane), collinear, coplanar, line segment, ray, midpoint, endpoint, bisect, congruent segment, acute, obtuse, right, straight, vertex, degree, angle bisector, congruent angles, vertical angles, linear pairs, complementary angles, supplementary angles, counterexample, and consecutive interior angles.

**AST 2.3 - Apply Symbols** : Correctly apply the following symbols and correct notation including but not limited to: congruency marks on a diagram, parallel and perpendicular indicators, designating lines, segments, and rays, equal, congruent, not congruent, etc. to interpret and solve problems.

**AST 2.4 - Congruent Circles** : This includes the use of congruent circles, concentric circles, radius, chord, diameter, tangent, point of tangency, central angle, and inscribed angle.

**AST 2.5 - Use Definitions and Postulates** : Use definitions and postulates to build and defend a logical argument.

ALT 3 - Congruence Theorems

I can prove and apply congruence theorems dealing with angles and lines to solve problems and justify my solutions.

**AST 3.1 - Apply and Prove Theorems** : Apply and prove theorems and use properties dealing with vertical angles and a linear pair of angles.

**AST 3.2 - Complementary and Supplementary Angles** : Apply and prove theorems and use properties dealing with complementary and supplementary angles.

**AST 3.3 - Paralel and Perpendicular Lines** : Apply and prove theorems and use properties dealing with parallel and perpendicular lines.

**AST 3.4 - Use Angle Measures to Prove Lines** : Use angle measures to prove lines parallel and perpendicular.

**AST 3.5 - Use Theorems to Justify Steps** : Use theorems to justify steps taken in finding missing measures.

ALT 4 - Congruence Theorems and Triangles

I can prove and apply congruence theorems dealing with triangles to solve problems and justify my solutions.

**AST 4.1 - Use Diagram Congruent Segments** : I can use a diagram that marks the congruent segments and angles and determine if two triangles are congruent.

**AST 4.2 - Prove Triangles Congruent** : I can use a diagram that marks the congruent segments and angles and formally prove if two triangles are congruent.

**AST 4.3 - Congruent Triangles Theorem** : I can use Corresponding Parts of Congruent Triangles Theorem to determine and prove other statements.

**AST 4.4 - Justify Steps Taken Missing Measures** : I can use theorems to justify steps taken in finding missing measures.

**AST 4.5 - Understand Origins of Points** : Understand origins of points of concurrency (Centroid, Incenter, Circumcenter and Orthocenter) of a triangle.

ALT 5 - Right Triangles

I can solve for unknown lengths and angles in right triangles and justify my solutions.

**AST 5.1 - Deterinme if Triangle can be Created** : Determine, if given three side lengths, a triangle can be created and justify my thinking.

**AST 5.2 - Use the Pythagorean Theorem ** : Use the Pythagorean Theorem to find unknown lengths of right triangles and whether the triangle is right, obtuse or acute and justify my thinking.

**AST 5.3 - Special Right Triangles** : Demonstrate and use properties of “special” right triangles (45-45-90, 30-60-90)

**AST 5.4 - Use Trigonemtric Ratios** : Use trigonometric ratios (sine, cosine, and tangent) to find the unknown lengths in right triangles.

**AST 5.5 - Find Unknown Angles in Right Triangles** : Use trigonometric ratios (sine, cosine, and tangent) to find the unknown angles in right triangles.

**AST 5.6 - Solve Right Triangles in Applied Problem** : Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

ALT 6 - 2-D Figures to Solve Problems

I can utilize the properties of two-dimensional figures to solve problems, including real-world applications.

**AST 6.1 - Classify and Compare Polygons** : Classify and compare polygons (quadrilaterals, in particular) based on characteristics.

**AST 6.2 - Prove Theorems about Quadrilaterals** : Prove theorems about quadrilaterals (opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelograms with congruent diagonals-using triangle congruence).

**AST 6.3 - Find Perimeter and Area of Polygons** : Find the perimeter and area of a variety of polygons, including applications.

**AST 6.4 - Find Unknown Sides and Angles** : Find the unknown sides and angles of a variety of polygons, including applications.

**AST 6.5 - Apply Congruence of Polygons** : Apply the congruence of polygons to solve problems.

**AST 6.6 - Find Area of Shaded Region** : Find the area of the shaded region (shapes within shapes) and composite areas.

**AST 6.7 - Find Arc Length and Areas** : Use formulas to find the arc length and area of sectors.

ALT 7 - Connect Linear Algebra

I can connect linear algebra, coordinates, and transformations to geometric situations and use it to prove geometric theorems.

**AST 7.1 - Use Coordinates to prove Geom. Theorems** : Use coordinates to prove simple geometric theorems algebraically and solve problems.

**AST 7.2 - Solve Associated Geo. Problems** : Determine that lines are parallel and perpendicular using the slope criteria and solve associated geometric problems.

**AST 7.3 - Find Missing Coordinates** : Given Midpoint or Distance, find the missing coordinates.

**AST 7.4 - Use Coordinates to Compute Perimeters** : Use coordinates to compute perimeters of polygons e.g., using the distance formula.

**AST 7.5 - Compute Areas of Triangles-Rectangles** : Use coordinates to compute the areas of triangles and rectangles, e.g., using the distance formula.

**AST 7.6 - Prove Theorems about Quadrilaterals** : Prove theorems about quadrilaterals using coordinates (opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelograms with congruent diagonals).

**AST 7.7 - Identify Lines of Symmetry** : Identify lines of symmetry and distinguish between rotation and reflection symmetries given a rectangle, parallelogram, trapezoid, or regular polygon

**AST 7.8 - Identify Rigid Transformations** : Identify and represent rigid transformations of 2-dimensional figures on and off the coordinate plane. (Translations, Reflections over either axis and y=x, Rotations in multiples of 90o)

**AST 7.9 - Identify Non-Rigid Transformations** : Identify and apply non-rigid transformations of geometric figures on and off the coordinate plane. (Dilation)

ALT 8 - 3-D Figures to Solve Problems

I can apply the characteristics and properties of 3-Dimensional figures to solve problems (including applications) and justify my solutions.

**AST 8.1 - Classify 3-D Figures from a Model** : Identify and classify 3-Dimensional figures from a model, a net, and different perspectives.

**AST 8.2 - Find Surface Area of 3-D Figures** : Find the surface area of 3-Dimensional figures, including applications.

**AST 8.3 - Find Volume of 3-D Figures** : Find the volume of 3-Dimensional figures, including applications.

**AST 8.4 - Identify Relationship Between 3-D-2-D** : Identify the relationships between 2-D and 3-D figures using cross-sections and rotations.

ALT 9 - Laws of Similarity to Solve Problems

I can apply the laws of similarity to solve problems and prove my solutions.

**AST 9.1 - Apply Similarity of Polygons** : Apply the similarity of polygons to solve problems in context.

**AST 9.2 - Apply Triangle Similarity Theorems** : Apply the triangle similarity theorems (using AA, SSS and SAS) to solve problems in context.

**AST 9.3 - Prove Shapes are Similar** : Prove whether or not two shapes are similar.

**AST 9.4 - Compare-Compute Areas and Volumes** : Given similar figures, compare and compute their respective areas and volumes.

ALT 10 - Probability to Interpret Data

I can use independence and conditional probability formally to interpret data and compute the probabilities of compound events.

**AST 10.1 - Describe Events as Subsets ** : Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or”, “and”, “not”).

**AST 10.2 - Demonstrate** : Demonstrate that P(A and B) = P(A)*P(B)

**AST 10.3 - Compute Complex Probabilities** : Use general formulas to compute complex probabilities (“or”, “and”, “not”).

**AST 10.4 - Use a Two-Way Table** : Use a two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.

**AST 10.5 - Concepts of Conditional Probability** : Recognize, explain, and model (Venn Diagrams and Tree Diagrams) the concepts of conditional probability and independence.

ALT 11 - Communication

Communicates clearly and explains reasoning so others can follow how a problem is solved.

ALT 12 - Problem Solving

Reasons mathematically to solve problems using patterns and models in both a pure and applied context.