Download New Title

You will need
10.5
•
•
•
•
•
Exploring Right Triangles
GOAL
0.5 cm grid paper
a protractor
scissors
a ruler
a calculator
Relate the lengths of the sides of right triangles.
Explore the Math
In regulation baseball, the distance
between adjacent bases is 90 feet.
This is about 27 m. Suppose that the
right fielder catches the ball while
standing on the foul line, 10 m from
first base. Then the right fielder
throws the ball to second base.
second base
■m
27
27
m
foul line
m
first
base
27
m
home plate
B. Measure the angles in the triangle. Which two angles are
complementary angles ?
C. Using 0.5 cm grid paper, cut out two squares to fit on the two short
sides of the triangle.
hypotenuse
the longest side of a
right triangle; the side
that is opposite the
right angle
F. Square the length of the hypotenuse to calculate a more precise value
for the area of the largest square.
G. Describe how the area of the largest square seems to compare with
the sum of the areas of the two smaller squares.
352 Chapter 10
nu
te
po
hy
E. Use a ruler to measure the hypotenuse to the nearest tenth of a
centimetre. Using 0.5 cm grid paper, cut out a square with that side
length. Estimate the area of the square.
se
D. Determine the area of each square by counting grid squares.
(Hint: Remember that each grid unit represents 1 m.)
leg
A. Draw a diagram like the one
above, on 0.5 cm grid paper.
Let one grid unit represent 1 m.
The red line, which is called
the hypotenuse , shows the
path of the ball.
third
base
m
fielder throws the ball,
without measuring?
pitching
rubber
27
can you calculate
? How
the distance that the right
10
m
right fielder
leg
complementary
angles
two angles whose
sum is 90°
NEL
H. How does the distance that the right fielder throws the ball relate to
the sum of the areas of the smaller squares?
Reflecting
1. Why are the two non-right angles in a right triangle always
complementary?
2. What did you learn when you compared the areas of the squares on
the three sides of the right triangle?
3. How does the length of the hypotenuse relate to the lengths of the
other two sides of a right triangle?
DISSECTING SQUARES
The area of the square on the hypotenuse of a right triangle is equal
to the sum of the areas of the squares on the other two sides. Did
you know that you can cut and rearrange the squares to show this?
You will need
• a ruler
• a protractor
A. Draw a right triangle, using a ruler and a protractor. Label the
sides of your triangle a, b, and c, where c is the side that is
opposite the right angle.
B. Draw squares on the sides of your triangle.
c
b
a
C. Draw the following lines through the square on side b:
• a line that extends one side of the square on c through the
square on b
• a line that is parallel to side c and passes through the vertex
opposite side c
b
c
a
D. Cut out all three squares. Then cut the square from side b
along the blue lines.
E. Fit square a and the pieces of square b into square c. What do
you notice? (Hint: Do not rotate the pieces.)
F. Try drawing other right triangles and dissecting the squares.
What do you notice?
NEL
Angles and Triangles
353