28 ft
45 ft
- PAPER AIRPLANE The figure below gives the
directions for making a paper airplane from a square
piece of paper with sides 8 inches long. Find the
length of the plane when it is completed in Step 3.
Round to the nearest hundredth.
- FIREFIGHTING The base of the 37-foot ladder
shown in the figure below is 9 feet from the wall. Will
the top reach a window ledge that is 35 feet above the
ground? Explain how you arrived at your answer.
- WIND DAMAGE A tree
was blown over in a wind
storm. Find the height of
the tree when it was standing
vertically upright.
WRITING
- State the Pythagorean theorem in your own words.
- When the lengths of the sides of the triangle shown
below are substituted into the equation ,
the result is a false statement. Explain why.
20 25
4 16 25
22 42 52
a^2 b^2 c^2
a^2 b^2 c^2
h ft
9 ft
37 ft
Step 1:
Fold
up.
Step 2:
Fold to make
wing.
Step 3:
Fold up tip
of wing.
8 in.
8 in.
8 in.
8 in.
length
- In the figure below, equal-sized squares have been
drawn on the sides of right triangle. Explain
how this figure demonstrates that.
- In the movie The Wizard of Oz,the scarecrow was in
search of a brain. To prove that he had found one, he
recited the following:
“The sum of the square roots of any two sides of an
isosceles triangle is equal to the square root of the
remaining side.”
Unfortunately, this statement is not true. Correct it so
that it states the Pythagorean theorem.
REVIEW
Use a check to determine whether the given number is a solution
of the equation.
53.
54.
55.
56.
57.
58.
59.
- 5 y 8 3 y2, 5
3 x 2 4 x5, 12
x
4
98 100, 8
33
x
2
30, 6
1.2x4.7, 3.5
0.5x2.9, 5
5 t 4 16, 2
2 b 3 15, 8
BA
C
32 42 52
ABC
9.4 The Pythagorean Theorem 753
2
4
5
