unit 6 lesson 1 the pythagorean theorem ccss g-srt 4: prove theorems about triangles. lesson goals...
TRANSCRIPT
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Unit 6 Lesson 1
The Pythagorean TheoremCCSS
G-SRT 4: Prove theorems about triangles.
Lesson Goals► Use the Pythagorean Th. to
find missing side lengths in a right triangle.
► Recognize a Pythagorean Triple.
ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers
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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.
ac
b
2 2 2c a b
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proof
A C
BD
af
ec
bStatement Reason
1. is a rt.ABC 2. Draw CD AB3. ~ ~CAB DAC DCB 4. ,
c a c b
a e b f
2 25. ,a ce b cf 2 26. a b ce cf 2 27. ( )a b c e f
8. c e f
1. Given
2. Perpendicular Post.3. Right D Altitude Th
4. Def similar polygons
5. Cross-Products Prop.6. Add. Prop. of =7. Distributive Prop8. Segment Add. Post
c
2 2 29. a b c 9. Substitution
2 2 2
Given: is a rt.
Prove:
ABC
a b c
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definition
Pythagorean Triples A set of three positive integers: a, b, c
that satisfy the equation
Examples
3, 4, and 5
5, 12, and 13
8, 15, and 17
2 2 2a b c
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6a
2 36a
2180 144a
22 26 5 12a
A C
B
a
12
6 5
example
Find the missing side
Do the side lengths form a Pythagorean Triple?
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You Try
Find the missing side
A C
B
7c
24
25c
2 625c
2 49 576c
2 2 27 24c
2 2 2c a b
Do the side lengths form a Pythagorean Triple?
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You Try
Find the missing side
19.06 10x
2 360x
441 81 x
2 2 221 9 x
2 2 2c a b
Do the side lengths form a Pythagorean Triple?
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39h
2 39h
2 25 64h
2 2 25 8h
Find the area of the triangle.
example
12A bh
12 10 39
25 39 m231 m
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You TryFind the area of the triangle
2 11x
2 44x
2144 100x
2 2 212 10x
12A bh
2 11 10 220 11 m
266.3 m
x2 112 11
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50 ft 50 ft100 ft
Two antennas are each supported by 100 foot cables. If the cables are attached to the antennas 50 feet fromthe ground, how far apart are the antennas?
d
100 ft
50 3x
2 7500x
2 2500 10,000x
2 2 250 100x
x
170 md 852d x
example
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summary
• How is the Pythagorean Theorem useful?
• What is the difference between the Pythagorean Theorem in general and a Pythagorean Triple?
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Today’s Assignment
p. 538: 8, 14, 18 – 28 e, 31 – 33, 37
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Find the unknown side length. Simplify answers that are radicals. Tell whether the side lengths form a Pythagorean triple.
Find the area of the figure. Round decimal answers to the nearest tenth.
Find the value of x. Simplify answers that are radicals.
The variables r and s represent the lengths of the legs of a right triangle, and t represents the length of the hypotenuse. The values of r, s, and t form a Pythagorean triple. Find the unknown value.