Geometry: An Interactive Journey to Mastery

(Greg DeLong) #1

  1. $UHJXODUKH[DJRQDOKROHLVFXWIURPDSDQRIEURZQLHVWKDWZHUHEDNHGLQDUHJXODUGHFDJRQDOSDQͼ௘7KH
    FHQWHUVRIWKHKH[DJRQDQGWKHGHFDJRQGRQRWFRLQFLGH௘ͽ,VWKHUHDVWUDLJKWOLQHFXWWKDWLVVXUHWRGLYLGH
    ZKDWUHPDLQVRIWKHEURZQLHVH[DFWO\LQKDOI",IVRJLYHDVLPSOHGHVFULSWLRQRIKRZWR¿QGWKDWOLQH

  2. $UHJXODUKH[DJRQDOKROHLVFXWIURPDSDQRIEURZQLHVWKDWZHUHEDNHGLQDUHJXODUGHFDJRQDOSDQͼ௘7KH
    FHQWHUVRIWKHKH[DJRQDQGWKHGHFDJRQGRQRWFRLQFLGH௘ͽ,VWKHUHDVWUDLJKWOLQHFXWWKDWLVVXUHWRGLYLGH
    what remains of the brownies exactly in half in area and divide the perimeter of the hole exactly in half and
    divide the perimeter of the decagon exactly in half?

  3. Given 40 inches of string, what shape for it encloses the largest
    DUHDRIÀRRULQDFRUQHURIDURRPEHWZHHQWZRSHUSHQGLFXODUZDOOV"
    ͼ௘6HHFigure 32.3௘ͽ

  4. A point is chosen at random inside a square. Line segments from it to
    each of the four corners of the square divide the square into four triangles.
    ͼ௘6HHFigure 32.4௘ͽ
    If two opposite triangles are shaded gray and the remaining two opposite
    triangles are shaded white, prove that the total portion of the square
    colored gray has the same area as the total portion colored white.

  5. Does every line through the center of an equilateral triangle cut the area of the triangle in half?


Problems

Figure 32.3

Figure 32.4
Free download pdf