Geometry Gap Summary

In order to eliminate gaps that will occur under the new core standards, we recommend the following changes be made in the 2012-13 and 2013-14 school year: (This material is not required under our current curriculum, but all material is available in our current textbook). 2013-14 will be the year for full implementation of the common core.

Proof: Integrated into curriculum 12-13
Construction: Integrated into curriculum 12-13
Probability: Integrated into Accelerated curriculum 12-13
Transformation Application: Integrated into curriculum 13-14
Coordinate Geometry: Integrated into curriculum 13-14
Conic Sections (Circles & Parabolas): Integrated into curriculum 13-14
Modeling: Integrated into curriculum 13-14

Geometry Gap Committee Recommendation
for PROOFS in 2012-13

Introduction to Proofs
*As a class, work 3 to 4 proofs from sections 2.6 and 2.7. This will serve as an introduction to proofs. Use the textbook/worksheet problems.

Parallel Line/Angle Pair Relationships
*Prove Theorem 3.1 in class (Pg. 134)
*Have students prove Theorems 3.2 and 3.3. Assign pg. 137 #39,40
*Prove Theorem 3.5 in class (Pg. 152)
*Have students prove either Theorem 3.6 or 3.7. Assign pg. 155 #32 or 33.

*Informally prove Theorem 4.1 (Triangle Sum Thm). Use technology (TI nSpire, Geomtry Sketchpad,etc), hands-on paper activity, protractor, etc.
*Prove triangles congruent using SSS, SAS, ASA, or AAS. Assign proofs similar to those on Pg. 204, 211. May supplement with worksheets.
*Prove Theorem 4.9 in class (Pg. 217)
*Have students prove Theorem 4.10. Assign Pg. 220 #33
*Have students prove Theorem 5.1. Assign Pg. 243 #10
*Informally show the points of concurrency for medians, altitudes, angle bisectors, and perpendicular bisectors. (i.e. have students construct, use TI Nspire, Geometry Sketchpad, etc.)
*Informal proof/demonstration of trigonometric ratios (see activity pg. 365)

*Prove Theorem 8.4 in class (Pg. 412)
*Have students prove Theorems 8.4-8.8. Assign pg. 415 #41-45 (pick 2)

*Derive arc length formula in class using Key Concept box on pg. 532
*Derive area of a sector formula in class using Key Concept box on pg. 623

Geometry Gap Committee Recommendation
for CONSTRUCTIONS in 2012-13

*Copy a Segment Page 15 (#48, 49 Page 18) Use compass/straightedge
*Bisect a Segment Page 24 (#2 Page 25) Use compass/straightedge
*Copy an Angle Page 31 Use compass/straightedge
*Bisect an Angle Page 33 Use compass/straightedge
*Perpendicular Line Page 44 (#1, 2 Page 44) Use compass/straightedge, calculator, software (you choose)
*Parallel Line Page 151 Use compass/straightedge, calculator, software (you choose)

*These constructions can be covered again when discussing Proof of Median, Altitude, Angle Bisector and Perpendicular Bisector Using compass/straightedge, calculator, software

Additional Resources
TI Nspire