5/22/17 Week 8 Monday daily sheet:
Pythagorean Theorem
Daily aims:
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1. I have memorized the Pythagorean Theorem and can identify the legs and hypotenuse.
2. I can calculate the length of the hypotenuse using the Pythagorean Theorem.
3. I can calculate the length of a missing leg using the Pythagorean Theorem.
4. I can solve word problems involving the Pythagorean Theorem
5. I can use knowledge of Pythagorean triples to bypass calculations with the Pythagorean Theorem.
Before lesson
1a) If c = 36 and c is positive, what’s the value of c?
During lesson
2
1b) If c2 = 42.25 and c is positive, what’s the value of c?
2b) The Pythagorean theorem helps you calculate…
a. angles
b. area
c. side length
2c) The Pythagorean Theorem applies ONLY to
______________________.
2a) Find the Pythagorean Theorem on your
formula sheet and write it here:
3) Find the length of the missing side (hypotenuse).
???
3 in
4 in
4) What are Pythagorean triples & why is it a timesaver
to know about them?
D. Stark 4/3/2017
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5a) Find the length of the missing side (leg)
10 cm
???
8 cm
5b) If one leg of a right triangle has a length of 2.2 m
and the hypotenuse is 4.5 m, to the nearest tenth,
what’s the length of the missing leg?
6) selected word problems from Number Power
geometry pp. 68-69.
D. Stark 4/3/2017
2
5/22/17 Week 8 Monday daily sheet:
KEY
Pythagorean Theorem
Before lesson
1a) If c = 36 and c is positive, what’s the value of c?
During lesson
2
6
1b) If c2 = 42.25 and c is positive, what’s the value of c?
6.5
2b) The Pythagorean theorem helps you calculate…
a. angles
b. area
c. side length
2a) Find the Pythagorean Theorem on your
formula sheet and write it here:
a2 + b2 = c2
Here a & b are the length of the legs (on either side
of the right angle) and c is the length of the
hypotenuse (the longest side—which is always
across from the right angle). It doesn’t matter
which you call a or b, but it does matter which is c.
3) Find the length of the missing side (hypotenuse).
a2 + b2 = c2
32 + 42 = c2
9 + 16 = c2
25 = c2
c = √𝟐𝟓
2c) The Pythagorean Theorem applies ONLY to
right triangles (triangles with 1 right angle).
A right angle is usually marked with a little square
in the corner, as in the diagram on the left.
???
3 in
4 in
c = 5 in.
D. Stark 4/3/2017
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4) What are Pythagorean triples & why is it a timesaver
to know about them?
Most Pythagorean problems don’t have nice whole
number answers. The ones that do are called
Pythagorean Triples. Math books and tests tend to
keep using variations on the few triangles that work
out nicely. The best one to know is the 3-4-5
triangle (leg of 3, leg of 4, hypotenuse of 5). Any
doubling, tripling etc. (6-8-10, 9-12-15) would also
be triples that you don’t have to memorize
separately. If you spot one, you can solve it without
going through the formula.
The 2nd most useful one to know is 5-12-13.
Finding the leg is harder than finding the
hypotenuse since it requires a little algebra.
5a) Find the length of the missing side (leg)
First, you could spot this as a
Pythagorean Triple and see
right away the answer is 6 cm.
(It’s a 6-8-10 triangle, just double
The 3-4-5 one.)
Otherwise, use the formula:
10 cm
8 cm
???
Notice that even if you’re squaring in the process,
the units on your final answers are regular units
(like inches, feet, cm, m), not square units. The
Pythagorean Theorem isn’t about area. It’s about
the length of sides, which is a distance.
a2 + b2 = c2
a2 + 82 = 102
a2+ 64 = 100
a2 + 64 = 100
a2 = 36
a = √𝟑𝟔
a = 6 cm
D. Stark 4/3/2017
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5b) If one leg of a right triangle has a length of 2.2 m
and the hypotenuse is 4.5 m, to the nearest tenth,
what’s the length of the missing leg?
a2 + b2 = c2
(2.2)2 + b2 = (4.5)2
4.84 + b2 = 20.25
4.84 + b2 = 20.25
b2 = 15.41
b = √𝟏𝟓. 𝟒𝟏
b  3.9 m
6) selected word problems from Number Power
geometry pp. 68-69.
See answers in back of the book.
D. Stark 4/3/2017
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