Below are the outcomes and specific skills you should have mastered during September - December of 2013. If you're looking to improve your "not-yets", practice the skills below during Intensives and your winter break. If you are able to prove to me that you are capable of applying these skills, I will change your outcome to a MS!
Keep in mind that this list is not necessarily representative of every type of problem you could see. However, if you understand these topics and can solve the suggested problems below, you are meeting standards for that outcome.
#1: Argues with different types of reasoning in order to prove or disprove a statement
#2: Discerns information about points, lines, and planes, including when they are parallel, perpendicular, intersecting or skew and uses appropriate notation and terminology
#3: Uses a straightedge and a compass to make precise constructions and can argue the validity of the construction
#4: Determines and uses the length and midpoint of a segment
#5: Graphically and algebraically discerns if lines are parallel or perpendicular on a coordinate plane and can identify the point of intersection of intersecting lines
#7: Discerns and applies theorems and relationships within triangles and communicates those relationships
#12: Applies and justifies properties of transformations and concepts of symmetry
- Prove that vertical angles are congruent
- Prove that alternate interior angles are congruent (when formed by two parallel lines cut by a transversal)
- Prove that alternate exterior angles are congruent (when formed by two parallel lines cut by a transversal)
- Prove that same-side interior angles are supplementary (when formed by two parallel lines cut by a transversal)
- Prove that same-side exterior angles are supplementary (when formed by two parallel lines cut by a transversal)
- Use the following definitions to complete basic proofs: definition of supplementary angles, definition of complementary angles, definition of perpendicular, definition of a midpoint
- Use the properties of equality to complete basic proofs (substitution, transitive, reflexive, addition, subtraction, multiplication, division)
#2: Discerns information about points, lines, and planes, including when they are parallel, perpendicular, intersecting or skew and uses appropriate notation and terminology
- Determine missing angle measures formed by parallel lines cut by a transversal (Practice: Parallel Lines 1, Parallel Lines 2)
- Use the angle addition postulate to solve problems
- Use the segment addition postulate to solve problems
- Understands and applies that a point on the perpendicular bisector of a segment is equidistant to the endpoints of that segment
- Understands and applies that a point on the angle bisector is equidistant to the sides of the angle
- Know that the distance from a point to a line is the perpendicular segment
#3: Uses a straightedge and a compass to make precise constructions and can argue the validity of the construction
- Construct the Perpendicular Bisector of a segment
- Construct a Perpendicular Line through a Point ON a Line
- Construct a Perpendicular Line through a Point OFF a line
- Construct a Parallel Line through a Point off a line (and justify it!)
- Construct the Angle Bisector of an angle
- Construct an Equilateral Triangle
- Circumscribe a circle about a triangle
- Inscribe a circle in a triangle
#4: Determines and uses the length and midpoint of a segment
- Given the endpoints of a segment, determine the coordinates of the midpoint
- Given the midpoint and one of the endpoints of a segment, determine the coordinates of the other endpoint of the segment
- Given the endpoints of a segment, determine the length of the segment (aka the distance between the two points)
- Derive the midpoint formula
- Derive the distance formula
#5: Graphically and algebraically discerns if lines are parallel or perpendicular on a coordinate plane and can identify the point of intersection of intersecting lines
#7: Discerns and applies theorems and relationships within triangles and communicates those relationships
- Identifies the median, angle bisector, perpendicular bisector, and altitude in a triangle
- Knows the names and properties of the points of concurrency of the medians, angle bisectors, perpendicular bisectors, and altitudes in a triangle (centroid, incenter, circumcenter, and orthocenter, respectively)
- Classifies triangles based on where the points of concurrency fall (example: The orthocenter falls on a right triangle, outside of an obtuse triangle, and inside an acute triangle)
#12: Applies and justifies properties of transformations and concepts of symmetry
- Find the image of a translated, rotated, reflected, or dilated point
- Identify transformations as an isometry or not (direct or opposite)
- Identify a transformation that has taken place
- Identify symmetries within shapes
- Understands and applies compositions of transformations, including appropriate notation