Targets & Standards
Geometry is a way to understand the real world around us by basing arguments on concrete referents, modeling relationships, and applying mathematical principles to understand geometric properties and concepts using objects, drawings, diagrams, and actions.
Essential Standards
G-CO.C Prove geometric theorems.
[Focus on validity of underlying reasoning while using variety of ways of writing proofs.]
G-CO.D Make geometric constructions. [Formalize and explain processes.]
G-CO.1 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.
There are no substandards for this standard.
G-CO.C Prove geometric theorems.
G-CO.9 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.
G-CO.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.
G-CO.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.
G-CO.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.
There are no substandards for this standard.
G-GPE.5 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).
There are no substandards for this standard.
Claim 3 (DOK 2, 3 & 4) Communicating Reasoning:
Students clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.
Assessment Targets (incorporate as many as possible)
Task Models & Examples (two samples to get the idea)
Supporting Standards
G-GPE.4 Use coordinates to prove simple geometric theorems algebraically.
For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, sqrt3) lies on the circle centered at the origin and containing the point (0, 2).
G-GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
Modeling standard linking mathematics to everyday life, work, and decision making.
G-GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
There are no substandards for this standard.
G-C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
There are no substandards for this standard.