Download Pythagorean Theorem: If ΔABC is a right triangle with legs a and b

Pythagorean Theorem: If ΔABC is a right triangle with legs
a and b and hypotenuse c, then
a2 + b2 = c2
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Converse of the Pythagorean Theorem:
If a2 + b2 = c2 (where a, b, and c are sides of ΔABC and c is
the longest side), then
ΔABC is a right triangle (with hypotenuse c)
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c
a
b
Do the following side lengths form a right
triangle?
2.) 8, 10, 241
1.) 11, 20, 23
112 + 202 ≟ 232
82 + 102 ≟ (241) 2
121 + 400 ≟ 529
64 + 100 ≟ 4x41
521≠ 529
164 = 164
No!
Yes!
Theorem 7.3: If a2 + b2 > c2 (where a, b, and c are sides of
ΔABC and c is the longest side), then
ΔABC is acute
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Theorem 7.4:
If a2 + b2 < c2 (where a, b, and c are sides of ΔABC and c is
the longest side), then
ΔABC is obtuse
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Explain why these Theorems are true
5
4.3
3
3
4
4
6
3
4
Can I make an obtuse triangle with
sides 3, 4, and 7?
Classify as acute, obtuse, or right
(approx: 3.6)
2.) 13, 10, 12
1.) 20, 21, 28
202 + 212 _____ 282
400 + 441 _____ 784
(13)2 + 102 _____ 122
13 + 100 _____ 144
113 < 144
841 > 784
Obtuse
Acute
20
21
28
3.6
10
12
Geometric Mean
For any two positive numbers a and b, the geometric
mean is the positive number x:
𝑎 𝒙
=
𝒙 𝑏
What is x = ?
𝑥 = 𝑎𝑏
Geometric Mean
𝑎 𝒙
=
𝒙 𝑏
𝑥 = 𝑎𝑏
What is the geometric mean of 2 and 25?
𝑥 = 50 = 5 2
The geometric mean of (2x – 2) and (x – 2) is (x + 2).
Find x