Topic: Congruence |
Common Core Mathematics 9-12 |
| Cluster Experiment with transformations in the plane |
| | Grade 9-12 |
| | | 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. |
| | | G.CO.2. | 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). |
| | | G.CO.3. | Given a rectangle, parallelogram, trapezoid, or regular polygon,
describe the rotations and reflections that carry it onto itself. |
| | | G.CO.5. | 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. |
| Cluster Understand congruence in terms of rigid motions |
| | Grade 9-12 |
| | | G.CO.6. | 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. |
| | | G.CO.7. | 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. |
| | | G.CO.8. | Explain how the criteria for triangle congruence (ASA, SAS, and SSS)
follow from the definition of congruence in terms of rigid motions. |
| Cluster Prove geometric theorems |
| | Grade 9-12 |
| | | 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. |
| Cluster Make geometric constructions |
| | Grade 9-12 |
| | | 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. |
| | | G.CO.13. | Construct an equilateral triangle, a square, and a regular hexagon
inscribed in a circle. |