The Nature of Mathematics, 12th Edition
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Section 7.4 Homework Hints

    Problems 1-2
    There are many problems throughout the text labeled IN YOUR OWN WORDS. Just relax; do not be afraid to give your opinion. For the most part, these questions do not have "right" or "wrong" answers. You should spend about five minutes in answering each of these questions.
    Problems 3-8
    Find two angles of one triangle congruent to two angles of another triangle to show that the triangles are similar. See Example 1.
    Problems 9-14 
    Be sure to orient the corresponding parts before answering.
    List the corresponding parts.
    Problems 15-20 
    Be sure to orient the corresponding parts before answering. List the corresponding parts and then find the lengths of the missing sides.

    For example, in Problem 15 , triangle ABC is similar to triangle DEF, so the length of segments AB to DE is proportional to the length of segments AC to DF. This means that the length DE must be 22 units. Similarly, the length of EF is 10 units. Now, you can list the lengths of all six parts.

    Problems 21-28
    See Example 2; draw a sketch similar to Figure 7.43, and then label the given distances before beginning.
    Problems 29-34
    First, identify the two triangles.  Determine that the two triangles are similar.
    Then, set up a proportion using corresponding parts of similar triangles. 
    See Example 2.
    Problem 35
    Mentally orient triangle ABM and triangle CBM to align corresponding parts. The right angles in each are congruent, so you need to find one additional pair of congruent angles.
    Problem 36
    Mentally orient triangle ADC and triangle CEA to align corresponding parts. It is given that the measures of angles D and E are equal, so you need to find one additional pair of congruent angles. 
    Problems 37-38
    Mentally orient the triangles to align corresponding parts. You must find two angles of one triangle congruent to two angles of the other triangle.
    Problems 39-53
    See Example 3; be sure to draw a figure for each problem.

    Note: Homework Hints are given only for the Level 1 and Level 2 problems.

    However, as you go through the book be sure you look at all the examples in the text. If you need hints for the Level 3 problems, check some sources for help on the internet (see the LINKS for that particular section. As a last resort, you can call the author at (707) 829-0606.

    On the other hand, the problems designated "Problem Solving" generally require techniques that do not have textbook examples.

    There are many sources for homework help on the internet.

    Algebra.help
    Here is a site where technology meets mathematics. You can search a particular topic or choose lessons, calculators, worksheets for extra practice or other resources.
    http://www.algebrahelp.com/

    Ask Dr. Math
    Dr. Math is a registered trademark. This is an excellent site at which you can search to see if your question has been previously asked, or you can send your question directly to Dr. Math to receive an answer.
    http://mathforum.org/dr/math/
    Quick Math
    This site provides online graphing calculators. This is especially useful if you do not have your own calculator.
    http://www.quickmath.com/

    The Math Forum @ Drexel
    This site provides an internet mathematics library that can help if you need extra help. For additional homework help at this site, click one of the links in the right-hand column.
    http://mathforum.org/

    Mathematics Home Page
    Access the Clemens and Alcuins Library of CSB/SJU and find one of the world's best collections of mathematical internet sites.
    http://library.csbsju.edu/rqs.phtml?subject_id=32

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