Mathsheets
Printable math worksheets for teachers and families
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Why the Pythagorean Theorem Works
Work in areas: the two smaller squares together fill the largest.
Example
A right triangle has legs of 3 and 4. Squares are drawn on the two legs.
b² = 16
a² = 9
c² = ?
b
= 4
a
= 3
Find the area of the square on each leg, then the area of the square on the hypotenuse. What is the hypotenuse?
a
² =
9
b
² =
16
c
² =
25
hypotenuse =
5
1.
A right triangle has legs of 3 and 4. Squares are drawn on the two legs.
b² = 16
a² = 9
c² = ?
b
= 4
a
= 3
Find the area of the square on each leg, then the area of the square on the hypotenuse. What is the hypotenuse?
a
² =
b
² =
c
² =
hypotenuse =
2.
A right triangle has legs 8 and 15 and hypotenuse 17.
Explain why
a
² +
b
² =
c
² is a statement about areas, and check it with these numbers.
Check:
Why areas?
3.
A triangle has sides
5, 12 and 13
. Is it a right triangle? Show how you know.
yes
no
Check:
Why?
4.
A right triangle has legs of 9 and 12. Squares are drawn on the two legs.
b² = 144
a² = 81
c² = ?
b
= 12
a
= 9
Find the area of the square on each leg, then the area of the square on the hypotenuse. What is the hypotenuse?
a
² =
b
² =
c
² =
hypotenuse =
5.
A triangle has sides
8, 15 and 17
. Is it a right triangle? Show how you know.
yes
no
Check:
Why?