Geometry for the Classroom: Exercises and Solutions

ISBN-13: 9780387975658 / Angielski / Miękka / 1991 / 180 str.

C.Herbert Clemens;Michael A. Clemens

Opis

Suitable for college courses for prospective or in-service secondary school teachers of geometry, this workbook contains solutions and commentary to the numerous exercises in the accompanying workbook.

Spis treści

Intuition.- I1e: Geometry is about shapes..- I2e: … and more shapes..- I3e: Polygons in the plane.- I4e: Angles in the plane.- I5e: Walking north, east, south, and west in the plane.- I6e: Areas of rectangles.- I7e: What is the area of the shaded triangle?.- I8e: Adding the angles of a triangle.- I9e: Pythagorean theorem.- Il0e: Side Side Side (SSS).- I12e: Rectangles between parallels and the Z-principle.- I13e: Areas: The principle of parallel slices.- I14e: If two lines in the plane do not intersect, they are parallel.- I15e: The first magnification principle: preliminary form.- I16e: The first magnification principle: final form.- I17e: Area inside a circle of radius one.- I18e: When are triangles congruent?.- I19e: Magnifications preserve parallelism and angles.- I20e: The principle of similarity.- I21e: Proportionality of segments cut by parallels.- I22e: Finding the center of a triangle.- I23e: Concurrence theorem for altitudes of a triangle.- I24e: Inscribing angles in circles.- I25e: Fun facts about circles, and limiting cases.- I26e: Degrees and radians.- I27e: Trigonometry.- I28e: Tangent ? =(rise)/(run).- I29e: Everything you always wanted to know about trigonometry but were afraid to ask.- I30e: The law of sines and the law of cosines.- I31e: Figuring areas.- I32e: The second magnification principle.- I33e: Volume of a pyramid.- I34e: Of cones and collars.- I35e: Sphereworld.- I36e: Segments and angles in sphereworld.- I37e: Of boxes, cylinders, and spheres.- I38e: If it takes one can of paint to paint a square one widget on a side, how many cans does it take to paint a sphere with radius r widgets?.- I39e: Excess angle formula for spherical triangles.- I40e: Hyperbolic-land.- Construction.- C1e: Copying triangles.- C2e: Copying angles.- C3e: Constructing perpendiculars.- C4e: Constructing parallels.- C5e: Constructing numbers as lengths.- C6e: Given a number, construct its square root.- C7e: Constructing parallelograms.- C8e: Constructing a regular 3-gon and 4-gon.- C9e: Constructing a regular 5-gon.- C10e: Constructing a regular 6-gon.- C11e: Constructing a regular 7-gon (almost).- C12e: Constructing a regular tetrahedron.- C13e: Constructing a cube and an octohedron.- C14e: Constructing a dodecahedron and an icosahedron.- C15e: Constructing the baricenter of a triangle.- C16e: Constructing the altitudes of a triangle.- C17e: Constructing a circle through three points.- C18e: Bisecting a given angle.- C19e: Putting circles inside angles.- C20e: Inscribing circles in polygons.- C21e: Circumscribing circles about polygons.- C22e: Drawing triangles on the sphere.- C23e: Constructing hyperbolic lines.- Proof.- P1e: Distance on the line, motions of the line.- P2e: Distance in the plane.- P3e: Motions of the plane.- P4e: A list of motions of the line.- P5e: A complete list of motions of the line.- P6e: Motions of the plane: Translations.- P7e: Motions of the plane: Rotations.- P8e: Motions of the plane: Vertical flip.- P9e: Motions of the plane fixing (0,0) and (a,0).- P10e: A complete list of motions of the plane.- P11e: Distance in space.- P12e: Motions of space.- P13e: The triangle inequality.- P14e: Co-ordinate geometry is about shapes and more shapes.- P15e: The shortest path between two points….- P16e: The unique line through two given points.- P17e: Proving SSS.