Download 3/5/2012 What`s New in Geometry *take out parallel planes and

3/5/2012
What’s New in Geometry
1. Geometric
Relationships
2. Logic and
Proof
3. Coordinate
Geometry
• *take out parallel planes and lines perpendicular to a
plane. (all the 3-D material)
• *Start proofs using parallel lines, transversals, and
angles (do this now instead of during Quads chapter)
• Prove theorems from G.CO- 9: vertical angles are
congruent, when a transversal crosses parallel lines,
alternate interior angles are congruent.
•Prove Triangle Midsegment Theorem (G.CO.10)
•Define Trig Ratios and solve problems using right triangles
(G.SRT.6)
•If two triangles are similar, the trig ratios for each pair of
corresponding angles will be the same.
•Prove Triangle Proportionality theorem and it’s converse
(G.SRT.4)
•Prove Pythagorean Theorem using similar triangles (draw in
altitude to hypotenuse, and set up ratios between the similar
triangles) (G.SRT.4)
•Proveing theorems about quadrilaterals (G.CO.11)
• Point on Segment, partitioning into given ratio (G.GPE.6)
• Completing the square (to find center and radius) (G.GPE.1)
• Derive equations of parabola given focus and direterix
(G.GPE.2)
• Use coordinates to compute perimeters of polygons and
areas of triangles and rectangles. (G.GPE.7)
• Deconstruction of compositions (G.CO.5)
• Given quadrilaterals/regular polygons, describe how to
reflect/rotate onto itself
• *Removed* Linear/quad systems graphically
3/5/2012
4.
Tranformational
Geometry
• *Removed* Linear/quad systems graphically
5. Circles
• *New* Prove that all cirles are similar. (G.C.1)
• *New and Hard* Construct the inscribed &
circumscribed circles of a triangle and prove properties
of angles for a quadrilateral inscribed in a circle. (G.C.3)
• Derive using similarity of arcs that are intercepted by
an angle is proportional to the radius (G.C.5)
• Derive the formula for the area of the sector (G.C.5)
6. Geometric
Relationships
•*Hard and New: Give an informal argument for formulas for
the circumference of a circle, area of a circle, voume of a
cylinder, pyramid & cone. Use dissection, arguments,
Cavalieri's principle, & limit arguments (G.GMD.1)
•Identify shapes of 2-D x-sections of 3-D objects & identify 3D objects generated by the rotation of 2-D objects.
(G.GMD.4)
•Apply concepts of density based on area & volume in
modleling situations (person/sq.mi) (G.MG.2)
•Apply geometric methods to design problems (G.MG.3)
7. Constructions
• Construct an equilateral triangle, a
square & a regular hexagon inscribe in a
circle.
• *Out* Locus
 Understand independence and conditional probability
and use them to interpret data.Link to data from
simulations or experiments S.CP.1, 2, 3, 4,
8. Probability
 Use the rules of probability to compute probabilities
of compound events in uniform probability model.
 Use probability to evaluate outcomes of decisions.
(Introductory; apply counting rules (+) S.MD.6,7