Download Classifying Triangles by Angles - Mr.Kerley`s class Mr.Kerley`s class

07-NelsonMathGr5-Chap07
6/24/04
2:47 PM
Page 194
CHAPTER 7
3
Classifying Triangles
by Angles
A. Triangles can be classified as right-angled,
obtuse-angled, or acute-angled triangles.
Classify Teresa’s roof triangles by the sizes
of their angles.
You will need
• a ruler
• a protractor
Goal
B. Draw three roof triangles of different steepness.
Investigate angle measures in triangles.
Roofs have different shapes.
Some roofs are steep so that
snow slides off easily.
C. Measure the three angles of each triangle.
Label the angle measures.
roof peak
D. Classify your triangles by the sizes of their angles.
E. How do the measures of the peak angles change as
the roofs get steeper?
does the angle at
? How
the peak relate to the
steepness of the roof?
Teresa’s Solution
right-angled
triangle
A triangle with one
right angle
Reflecting
right angle
The angle made
by a square corner.
A right angle
measures 90º.
1. Which angle would you measure first to classify
each triangle? Why?
a)
A
acute-angled
triangle
A triangle with only
acute angles
I’ll draw roof triangles with different angles at the peak.
Triangle A has a right angle.
C
90°
A
Triangle B has an obtuse angle.
It’s not as steep as triangle A.
obtuse-angled
triangle
A triangle with one
obtuse angle
B
obtuse angle
An angle that
measures greater
than 90º
F
b)
D
E
B
The angles in triangle C are all acute angles.
It’s steeper than triangles A and B.
135°
c)
acute angle
An angle that
measures less
than 90º
I
H
2. Do you need to measure all three angles to classify
a triangle? Explain your answer.
C
45°
194
G
NEL
NEL
195
07-NelsonMathGr5-Chap07
6/24/04
2:47 PM
Page 194
CHAPTER 7
3
Classifying Triangles
by Angles
A. Triangles can be classified as right-angled,
obtuse-angled, or acute-angled triangles.
Classify Teresa’s roof triangles by the sizes
of their angles.
You will need
• a ruler
• a protractor
Goal
B. Draw three roof triangles of different steepness.
Investigate angle measures in triangles.
Roofs have different shapes.
Some roofs are steep so that
snow slides off easily.
C. Measure the three angles of each triangle.
Label the angle measures.
roof peak
D. Classify your triangles by the sizes of their angles.
E. How do the measures of the peak angles change as
the roofs get steeper?
does the angle at
? How
the peak relate to the
steepness of the roof?
Teresa’s Solution
right-angled
triangle
A triangle with one
right angle
Reflecting
right angle
The angle made
by a square corner.
A right angle
measures 90º.
1. Which angle would you measure first to classify
each triangle? Why?
a)
A
acute-angled
triangle
A triangle with only
acute angles
I’ll draw roof triangles with different angles at the peak.
Triangle A has a right angle.
C
90°
A
Triangle B has an obtuse angle.
It’s not as steep as triangle A.
obtuse-angled
triangle
A triangle with one
obtuse angle
B
obtuse angle
An angle that
measures greater
than 90º
F
b)
D
E
B
The angles in triangle C are all acute angles.
It’s steeper than triangles A and B.
135°
c)
acute angle
An angle that
measures less
than 90º
I
H
2. Do you need to measure all three angles to classify
a triangle? Explain your answer.
C
45°
194
G
NEL
NEL
195
07-NelsonMathGr5-Chap07
6/24/04
2:47 PM
Page 196
Curious Math
Checking
3. a) What type of triangle has an angle that measures
120º and an angle that measures 30º?
b) What type of triangle has an angle that measures
20º and an angle that measures 90º?
Diagonal Angles
4. Classify the triangles by the sizes of their angles.
Measure the angles if necessary.
a)
b)
1 2 3 4 5 6
E
A
B
D
F
Measure and record the
angles where the diagonals
cross on the square and the
other rectangle.
H
G
C
Angle Measures
Square
Practising
5. Kumiko’s class made triangle name tags for open house.
Classify the triangles.
a)
c)
A
E
B
F
C
G
D
H
Erlwanger
d)
Gorman
1 2 3 4 5 6
1 2 3 4 5 6
Li
Draw two rectangles of
different sizes and measure
the angles where the
diagonals cross.
What conclusion can you make?
6. Look around the room. Find triangle shapes with different
kinds of angles.
a) Measure the sides and angles of the triangles.
b) Draw the triangles. Label the angles.
c) Classify the triangles according to their angle sizes.
7. Explain why you agree or disagree with each statement.
a) Glynis said, “My triangle has one right angle, so it is a
right-angled triangle.”
b) Martin said, “My triangle has one acute angle, so it is
an acute-angled triangle.”
c) Jose said, “My triangle has one obtuse angle, so it is
an obtuse-angled triangle.”
196
a) What do you notice
about the angles where
the diagonals of a square
cross?
b) What do you notice
about the angles of the
other rectangle?
Johnson
b)
1 2 3 4 5 6
Rectangle
NEL
NEL
Measure the lengths of the
diagonals in Question 1 from
the vertex to the point
where the diagonals cross.
What do you notice?
197