Geometry for the Classroom: Exercises and Solutions

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