E7 Students are expected to
recognize, name, describe, and
construct right, obtuse, and acute
triangles
Just as the rectangle and the circle are very
popular in the real world, so is the triangle!
You'll find triangles at work:
racking billiard balls
holding up a shelf
bracing a structure or bridge
"Cygnet #2, "a tetrahedral kite designed by D.
Alexander Graham Bell, built at Baddeck, Nova
Scotia, contains 3,960 tetrahedral cells covered with
red silk and driven by same motor as the Silver Dart.
http://www.digitaloutrider.com/html/bell/inventor.html#silver
A triangle is the simplest polygon, having
three sides and three angles. The sum of the
three angles of a triangle is equal to 180
degrees.Triangles are classified in two ways:
by their sides and by their angles.
Equilateral – three
sides equal. Side A =
Side B = Side C
Isosceles – two
equal sides Side
a equal in length
to Side b
Scalene – no
sides equal
A triangle is named not just from the size of
its angles, but also from the lengths of its
three sides.
A triangle with all sides of the same length is
called a(n) equilateral triangle.
The angles of this type of triangle are all equal.
Since the three angles of any triangle add up
to 180 degrees, then each angle in this special
type of triangle must be 180 divide by 3 or
60 degrees.
An equilateral triangle has three equal sides.
In this type of triangle, the angles are also
equal, so it can also be called an equiangular
triangle. Each angle of an equilateral triangle
must measure 60 degrees, since the sum of
the interior angles of any triangle must equal
180 degrees.
An isosceles triangle has just two equal sides,
called legs. The third side is called the base.
The angles that are opposite the equal sides
are also equal.
A triangle with three sides of different
lengths is called a scalene triangle. Its angles
are all of different sizes, as well.
Now let's classify by angles. An acute triangle has
three acute angles, or three angles with a measure of
less than 90 degrees. An obtuse triangle has one angle
that is greater than 90 degrees. If one of the angles in
a triangle is a right angle, then the triangle is called a
right triangle. Notice we draw a square at the vertex
where the right angle is located.
Obtuse – 1
obtuse angle
Acute – all three
acute angles
Right
–
1
right angle
You can use two labels for a triangle. For
example, triangle MNO is both an acute and
an isosceles triangle. Triangle PQR is an
obtuse, scalene triangle. Triangle ACB is a
right, scalene triangle.
Student Activities
A triangle is a polygon with three sides, three
angles, and three vertices.
Examine the different triangles given to you
according to the nature of their angles.
Share how you sorted the triangles.
What name is given to each of these triangles
when their angle sizes are considered?
Student Activities
Examine the tangram pieces. What is the
name of each of the pieces? How many
different types of triangles are represented
in a set of tangram pieces?
Use geostrips in your group to create as many
different triangle types as you can. Sketch
your creation using a ruler and then label the
triangle with its full name. e.g. right isosceles
triangle.
Tangram Pieces
How many different types of
triangles are represented in a
set of tangram pieces?
Student Activities
E7.1 Construct specific triangles on
a geoboard and record them on
geopaper, e.g., an acute triangle that
has one side using five pins, a right
triangle that is also isosceles, and an
obtuse triangle that has one side
using five pins.
Student Activities
E7.2 Draw three examples of each type of
triangle.
E7.3 Use two 6cm straws, two 8 cm straws,
and two 10cm straws to investigate the
triangles that can be made using 3 of the
straws at a time. Complete a table of results.
Extension: Use geostrips in your group to
create as many different triangle types as you
can. Sketch your creation using a ruler and
then label the triangle with its full name. e.g.
right isosceles triangle.