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Geometry And Topology

By John Casey

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Extra resources for A treatise on the analytical geometry of the point, line, circle, and conic sections, containing an account of its most recent extensions, with numerous examples.

Example text

Name four tools that are used in geometry. 3. 32 Chapter 1 Reasoning in Geometry Mario says that a straightedge and a ruler are the same. Curtis says they are different. Who is correct? Explain your reasoning. straightedge compass construction midpoint Guided Practice Examples 1 & 2 Use a straightedge or compass to answer each question. 4. Which segment on the upper left forms a straight line with the segment on the lower right? 5. Which is greater, the height of the hat (from A to B) or the width of the hat (from C to D)?

A Plan for Problem Solving A useful measurement in geometry is perimeter. Perimeter is the distance around a figure. It is the sum of the lengths of the sides of the figure. The perimeter of the room shown at the right is found by adding. 12 ft 9 ft 15 ft BEDROOM 6 ft P ϭ 12 ϩ 9 ϩ 6 ϩ 6 ϩ 18 ϩ 15 or 66 6 ft The perimeter of the room is 66 feet. 18 ft Some figures have special characteristics. For example, the opposite sides of a rectangle have the same length. This allows us to use a formula to find the perimeter of a rectangle.

30) construction (p. 30) coplanar (p. 14) endpoint (p. 13) formula (p. 35) four-step plan (p. 37) line (p. 12) line segment (p. 13) midpoint (p. 31) noncollinear (p. 13) noncoplanar (p. 14) Pascal’s triangle (p. 10) perimeter (p. 35) plane (p. 14) point (p. 12) postulate (p. 18) ray (p. 13) straightedge (p. 29) undefined terms (p. 12) conclusion (p. 24) conditional statement (p. 24) conjecture (p. 6) contrapositive (p. 28) converse (p. 25) counterexample (p. 6) hypothesis (p. 24) if-then statement (p.

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