Draft+Geometry+power+stds

**DRAFT Power Standards for Geometry based on the HSCEs**
Know the definitions of various quadrilaterals and their hierarchical relationships (G1.4.3) Know how angles are measured in circles, including basic concepts of arcs and chords; know how area and circumference of circles are calculated. Basic relationships include: · lines: angles on a line add to 180, vertical angles are equal, angle made by perpendicular lines equal 90, for parallel lines cut by a transversal, corresponding angles are equal · triangles: angles add to 180 · right triangles: Pythagorean theorem, definitions of sin, cos, tan · area of a rectangle is l ∙ w  The measure of an arc in degrees is defined as the same as its central angle; the length of the arc is in proportion to the circumference Complex relationships to be derived: · angles in quadrilaterals add to 360 · for parallel lines cut by a transversal, alternate interior angles are equal · base angles of isosceles triangle are equal, opposite angles of parallelogram are equal, base angles of isosceles trapezoid are equal · exterior angle of triangle equals sum of remote interior angles (G1.2.1) · know how to justify one or two simple constructions (G1.1.4) · prove congruence (G2.3.1-2) · properties of medians, altitudes and perpendicular bisectors in triangles (G.1.2.5) · derive sum of interior or exterior angles of polygons (G1.4.4) · prove the Pythagorean theorem (G1.2.3); prove side lengths in 30-60-90 and 45-45-90 triangles (G1.2.4) · derive formulas for area of various quadrilaterals (G2.1.1-2) · explain the relationship between central angles, inscribed angles and inscribed triangles (G1.6.3) Use coordinate geometry to construct proofs (G1.4.2); derive midpoint length of a segment (G1.1.5); solve problems using vectors (L1.2.3) Know the difference between statistical and logical arguments. (L3.1.2) Solve problems involving surface area and volume of pyramids, prisms, cones, cylinders, hemispheres and spheres (G1.8.1, G2.1.3) Solve problems (and explain reasoning) involving circles Use Pythagorean theorem (G1.2.3) Use coordinate geometry as needed (G2.3.4) Use law of sines, law of cosines, area of triangle = (G1.3.2) Find areas of polygons (G1.5.1); find perimeter and area of regular n-gons; find interior and exterior angles of regular n-gons (G1.5.2) Understand how figures can be scaled up or down and what effect this has on angle measures, perimeter and area: the area (volume) of a figure increases or decreases as the square (cube) of perimeter or side length. (G2.3.5) Use knowledge of central angles, inscribed angles (G1.6.3), arcs, sectors (G1.6.4), chords, tangents (G1.6.2), circumference and area (G1.6.1) http://www.1728.com/circsect.htm Contact Theron Blakeslee for more information or to make suggestions on this document, at tblakesl@inghamisd.org or 517-244-1201.
 * Know basic relationships ** regarding angles and sides in triangles; parallel and perpendicular lines; calculation of area and perimeter in rectangles and right triangles
 * Think logically. Know how to analyze and communicate logical arguments. ** Derive complex relationships from simpler ones, justifying each step with a logical argument. (i.e. construct proofs: G1.4.1)
 * Solve problems (and explain reasoning) ** involving angle measure (G1.1.1-2), side length, diagonal length, perimeter and area of various parallelograms, trapezoids and kites (G1.4.1), congruent and similar triangles (G2.3.2-3)