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A review of the key concepts and skills expected for the final exam in mth 202, focusing on geometry. Topics include counting vertices, edges, and faces of 3d shapes, determining angle measures, classifying relationships between triangles and quadrilaterals, understanding definitions of circles and spheres, basic constructions, platonic solids, translations, reflections, rotations, symmetry, triangle congruence conditions, proving results using congruent triangles, solving similarity problems, units of measurement, conversions, dimensions, calculating perimeters and areas, understanding rectangular formulas for area and volume, moving and additivity principles of area & volume, cavalieri’s principle, finding area and circumference of circles, approximating areas of irregular shapes, finding volume of irregular solids, and understanding the relationship between perimeter, area, figure, scaling, and similarity.
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MTH 202 · Final Exam (Minimal) Review CHAPTER 8 Be able to count the vertices, edges, and faces of 3D shapes. Be able to determine angle measures given a diagram (straight line 180, vertical angles, parallel postulate, triangle sum theorem). Be able to classify the relationships between triangles and quadrilaterals using Venn diagrams (this involves knowing the definitions). Know the definition of circle/sphere and be able to use them in problems. Be able to do basic constructions with straightedge and compass (e.g., perpendicular bisector, angle bisector, equilateral triangle, rhombus). Recall the Platonic Solids. o #3 on pg 412-413, #4 on pg 423, #14 on pg 437, #4 on pg 442-443. CHAPTER 9 Know everything about translations, reflections, and rotations (and don’t forget glide reflections, either). Be comfortable with all different types of symmetry. Understand the triangle congruence conditions, and be aware of situations that do not guarantee triangle congruence. Be able to prove a result using congruent triangles. Be able to solve similarity problems (scale factor, relative sizes, set-up-a- proportion). o #3 on pg 467, #9a on pg 468, #4 on pg 482, #1 on pg 491, #4 on pg 509, also practice proofs from the Extended 9.3 PDF available on the class website.
Be comfortable with units of measurement (standard and metric) and conversions. Understand the relationship between the size of the unit and the size of the measurement. Be aware of dimensions and how they relate to various measurements (e.g., length, area, and volume). Be able to calculate all sorts of perimeters and areas Be able to explain the rectangular formulas for area and volume. o #1 on pg 527, #6 on pg 539, #8 on pg 555, #14 on pg 555, #17 on pg 555. CHAPTER 11 Understand the moving and additivity principles of area & volume, as well as Cavalieri’s principle about shearing. Be able to solve complex area problems in a variety of ways. Be able to prove the Pythagorean Theorem. Understand the formulas for the area of a triangle, the area of a parallelogram, and the area of trapezoid (you should be able to justify the formulas in some way). Be able to find the area and circumference of circle (specifically, know what π is). Be able to approximate areas of irregular shapes, and find the volume of irregular solids. Understand the relationship between perimeter and area of a figure. Be able to find the surface area and volume of prisms and pyramids. Understand the relationship between scaling (i.e., similarity) and area/volume. o #16 on pg 574-575, #1 on pg 583, #8 on pg 594-595, #3 on pg 600, #3 on pg 606, #5 on pg 607, #5 on pg 616-617, #13 on pg 617-618, #3 on pg 623, #10 on pg 627, #6 on pg 636, #17 on pg 639, #4 on pg 644.