1. Proving Similarity via Transformations
Dilation is a Non-Rigid Transformation that preserves angle, but involves a scaling factor that affects the distance, which results in images that are similar to the original shape.
G-SRT Cluster Headings dealing with Similarity:
Understand Similarity in terms of similarity transformations
Prove theorems involving similarity

2. Proving Similarity via Transformations
From a transformational perspective… Two shapes are defined to be similar to each other if there is a sequence of rigid motions followed by a non- rigid dilation that carries one onto the other. A dilation formalizes the idea of scale factor studied in Middle School.

3. Prove Similarity by Transformations
What non-rigid transformation proves that these triangles are similar? What is the center of dilation? What is the scale factor of the Dilation?

4. Find Scale Factors Given a Transformation
Similarity Transformations Created by: Jacelyn O'Roark

5. Circles in Analytic Geometry
G-GPE (Expressing Geometric Properties with Equations)
Derive the equation of a circle given center (3,-2) and radius 6 using the Pythagorean Theorem
Complete the square to find the center and radius of a circle with equation x2 + y2 – 6x – 2y = 26
Think of the time spent in Algebra I on factoring
Versus completing the square to solve quadratic
Equations. What % of quadratics can be solved
by factoring? What % of quadratics can be
Solved by completing the square?
Is completing the square using the area model
more intuitive for students?

6. Conic Sections – circles and Parabolas
Translate between the geometric description and the equation for a conic section
Derive the equation of a parabola given a focus and directrix
Parabola – Note: completing the square to find the vertex of a parabola is in the Functions Standards
(+) Ellipses and Hyperbolas in Honors or Year 4
Sketch and derive the equation for the parabola with
Focus at (0,2) and directrix at y = -2
Find the vertex of the parabola with equation
Y = x2 + 5x + 7

7. Visualize relationships between 2-D and 3-D objects
Identify the shapes of 2-dimensional cross sections of 3- dimensional objects

8. Visualize relationships between 2-D and 3-D objects
Identify 3-dimensional shapes generated by rotations of 2-dimensional objects

9. North country Inservice outline
Review with Agreed Upon Expectations from Inservice – Share Experiences
Review of CCSSM Practice Standards – Share Experiences
Presentation of How Geometry Unfolds over K – 12 in CCSSM
Focus on Volume Standard in HS Geometry
Develop one unit focusing on HS Volume Standard and Practice Standards

10. HS.GMD.A.1
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.