The following are the 8 MOST important topics and associated concepts/skills you ought to be a Guru at for the CSET Subtest II Geometry:
1. Definitions, Postulates, Properties and Theorems: Basic knowledge and understanding of these is tested throughout the Multiple Choice section of Subtest II, and of course, these are vital for constructing Geometric Proofs!
You shall find a fairly exhaustive list of Definitions, Postulates, Properties and Theorems at other links on this site - Subtest II: Writing Geometry Proofs the Painless Way! and SUBTEST II: Geometry - 42 Vital Theorems!)
2.Properties of Parallel Lines: Proofs regarding Alternate Interior Angles, Alternate Exterior Angles and Consecutive Interior Angles and their Converse (ie. conditions for 2 lines to be parallel).
You MUST know in a very fundamental fashion when to use the Theorems themselves, and when their Converses: it can mean the difference between getting a question right (and passing!) and not. While proofs of parallel lines themselves are not asked, these form the building blocks of more advanced proofs, for instance, for sophisticated problems on triangle congruence, parallelograms and similar triangles.
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3. Congruence of Triangles: You are all but assured ONE question on this topic on the Free Response section, and it might call for application in a direct fashion - for instance, having to prove that corresponding parts of 2 triangles are congruent - or in an indirect manner - embedded in a question on parallelograms, perhaps.
Not infrequently, you may be provided with two pairs of triangles, and you have to show
a) the congruence of 1 pair to prove that
b) their corresponding parts are congruent, and use this fact to prove
c) the congruence of the second pair of triangles, and employ this, finally, to prove that
d) corresponding parts (sides/angles) of this pair are congruent!
4. Triangle Theorems and Properties: These relate to sides and angles of triangles in general, and for Isosceles and Right Triangles, in particular. This also includes Perpendicular Bisector, Angle Bisector, Median, and Mid-Segment Theorems.
5. Quadrilaterals and Parallelograms: This topic is a terrific assessment of your skills regarding Parallel Lines and Congruence of Triangles as they are indispenseable here! You ought to master the proofs about properties of Parallelograms and Rhombuses. Those on Rectangles, Squares, Trapezoids and Kites can be treated depending on the time you have, though I strongly recommend it if it can 'squeezed in'.
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Quick links: Articles Index, TESTIMONIALS & FEEDBACK and CONTACT ME!
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6. Transformations: This is a much neglected topic, but you ought have a robust grasp of elementary transformations like Reflection, Rotation and Translation, which are sometimes coupled with the Similarity concept of Dilation. Further, the Proofs on these transformations being isometries are VERY important!
7. Similar Polygons and Solids: Properties about their sides and angles; and Ratios of their Perimeters, Areas and Volumes (for similar solids). A passing acquaintance with Similar Triangles is sufficient.
8. Right Triangles: This topic concerns 2 Geometric Mean Theorems (using Similarity of Triangles), Pythagoras Theorem and Special Right Triangles (30-60-90 and 45-45-90), all of whose proofs I recommend that you know. Further, Right-Angle-Trigonometry is a fundamental skill area using which you can find the Areas and Perimeters of regular polygons, on which you're assured one, if not more questions!
As a general tip, Formulae of Areas of simple geometric figures and 3-dimensional solids are critically important and therefore useful to commit to memory, since they're not provided.
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