assignment p. 436-439: 1-17, 18-22 even, 28-31, 38-40 challenge problems
TRANSCRIPT
Parts of a Right Triangle
Which segment is the longest in any right triangle?
7.1 Apply the Pythagorean Theorem
Objectives:
1. To discover and use the Pythagorean Theorem
2. To use Pythagorean Triples to quickly find a missing side length in a right triangle
The Pythagorean Theorem
In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
The Pythagorean Theorem
In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
c 2
b 2
a 2
Example 2
The triangle below is definitely not a right triangle. Does the Pythagorean Theorem work on it?
m AC = 7.62 cm
m CB = 12.15 cm
m BA = 11.85 cm
6937
B
A
C
Example 3
How high up on the wall will a twenty-foot ladder reach if the foot of the ladder is placed five feet from the wall?
√375
Example 4: SAT
In figure shown, what is the length of RS?
7
3
RT
S
√4
Example 6
Find the area of the triangle.
h = 4
A=1/2bh
A=20
Pythagorean Triples
Three whole numbers that work in the Pythagorean formulas are called Pythagorean Triples.
Pythagorean Multiples
Pythagorean Multiples Conjecture:If you multiply the lengths of all three sides of
any right triangle by the same number, then the resulting triangle is a right triangle.
In other words, if a2 + b2 = c2, then (an)2 + (bn)2 = (cn)2.
Primitive Pythagorean TriplesA set of Pythagorean triples is considered a
primitive Pythagorean triple if the numbers are relatively prime; that is, if they have no common factors other than 1.
3-4-5 5-12-13 7-24-25 8-15-17
9-40-41 11-60-61 12-35-37 13-84-85
16-63-65 20-21-29 28-45-53 33-56-65
36-77-85 39-80-89 48-55-73 65-72-97
Example 9
Find the length of one leg of a right triangle with a hypotenuse of 35 cm and a leg of 28 cm.
x7=28
x7=35
21=7x
Example 10
Use Pythagorean Triples to find each missing side length.
Example 11
A 25-foot ladder is placed against a building. The bottom of the ladder is 7 feet from the building. If the top of the ladder slips down 4 feet, how many feet will the bottom slip out? Draw a picture