8.3. Using Similar Right Triangles http://www.ck12.org
- Mrs. Smith teaches AP Calculus. Between the first and second years she taught the course her students’
average score improved by 12%. Between the second and third years, the scores increased by 9%. What is the
average rate of improvement in her students’ scores? - According to the US Census Bureau, http://www.census.gov/ipc/www/idb/country.php the rate of growth of
the US population was 0.8% and in 2009 it was 1.0%. What was the average rate of population growth during
that time period?
Algebra ConnectionA geometric sequence is a sequence of numbers in which each successive term is determined
by multiplying the previous term by the common ratio. An example is the sequence 1, 3, 9, 27, ... Here each term is
multiplied by 3 to get the next term in the sequence. Another way to look at this sequence is to compare the ratios
of the consecutive terms.
- Find the ratio of the 2ndto 1stterms and the ratio of the 3rdto 2ndterms. What do you notice? Is this true for
the next set (4thto 3rdterms)? - Given the sequence 4, 8, 16,..., if we equate the ratios of the consecutive terms we get:^84 =^168. This means
that 8 is the of 4 and 16. We can generalize this to say that every term in a geometric
sequence is the of the previous and subsequent terms.
Use what you discovered in problem 26 to find the middle term in the following geometric sequences.
- 5, ____, 20
- 4, ____, 100
- 2, ____,^12
- We can use what we have learned in this section in another proof of the Pythagorean Theorem. Use the
diagram to fill in the blanks in the proof below.
TABLE8.4:
Statement Reason
1.ea=d+?eanddb=b? Theorem 8-7
2.a^2 =e(d+e)andb^2 =d(d+e)?
3.a^2 +b^2 =? Combine equations from #2.4.? Distributive Property
5.c=d+e?
6.? Substitution PoE
Review Queue Answers
- No, another angle besides the right angles must also be congruent.