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Geometry – Chapter 6 Lesson Plans
Section 6.5, 6.6 & 6.7 – Right Triangles, Pythagorean Theorem,
Distance Formula
Enduring Understandings: The student shall be able to:
1. use congruence tests for right triangles
2. use the Pythagorean theorem
3. find the distance between two point on the coordinate plane
Standards:
45. Coordinate Geometry
Applies the distance and midpoint formulas
26. Right Triangles
States and applies the Pythagorean Theorem and its converse.
Warm up/Opener:
Viewgraph 6.4
Essential Questions: What is special about right triangles?
Activities:
Lesson/Body:
6.5: We did what we need to do with congruence testing with right triangles already. We
did the HL. This chapter also includes LL (SAS), HA and LA (both AAS).
Pythagoreans:
1 represented logic because reason could produce only one consistent body of
truths
2 stood for man
3 stood for woman
4 stood for justice, because it was the first number to be the product of equals
5 was identified with marriage, formed as it was by the union of 2 and 3
6 was the number of creation, and so on.
All the even numbers, after the first even number, were separable into other
numbers – hence they were prolific and were considered feminine and earthly,
and somewhat less highly regarded in general.
And because the Pythagoreans were a predominantly male society, they classified
the odd numbers, after the first one, as masculine and divine.
Pythagorus Theorem: Prove it – pg 102 of my History of Math book.
Pythagorean Triples
Pythagorean Triples are integers that satisfy the a2 + b2 = c2 relationship.
The Babylonians knew of the relationship as shown on the clay tablet known as
the Plimpton 322, which is dated between 1900 B.C. and 1600 B.C. (History of
Math page 68)
Pythagoras (585-500 B.C.) had a partial solution of x = 2n + 1, y = 2n^2 + 2n, and z =
2n^2 + 2n + 1
Plato's (388 B.C.) determined a partial solution of x = 2n, y = n2 - 1, and z = n2 + 1
Neither of the above accounts for all the triplets, and it was not until Euclid wrote in his
Elements the following complete solution.
Euclid (323-285 B.C) in Book X of his Elements wrote the complete solution to the
Pythagorean triplet problem: X = 2NM Y = M^2 - N^2 Z = M^2 + N^2, where m and n
are positive integers, with m > n.
Diophantus wrote in his Arithmetica that he also derived Euclid's equations.
6.7 Distance formula is simply Pythagorean Theorem.
D = [(x2 – x1)2 + (y2 – y1)2]1/2
Assessments:
CW WS 6.6 & 6.7
HW
Pg 254, # 7 – 27 odd (11 problems)
pg 260-261, # 18-44 even (14 Problems)
Pg 266-267, # 12-12-34 evens (12 problems)