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Triangles
Warm Up
Tell if each figure is a polygon. If it is not a polygon,
explain why. If it is a polygon, name it and tell if it is
regular.
1).
3).
2).
Warm Up
Tell if each figure is a polygon. If it is not a polygon, explain
why. If it is a polygon, name it and tell if it is regular.
1).
2).
Nonagon,
Not regular
3).
Pentagon,
regular
Quadrilateral,
regular
4).
Not a
polygon, not
made of line
segments.
Classification of Triangles by Angles
Acute Triangle Right Triangle
Obtuse Triangle
Exactly one
Exactly one
All three
interior angles interior angle interior angle is
measures 90°. obtuse.
are acute.
Classification of Triangles by Sides
Scalene
Triangle
All sides have
different
lengths.
Isosceles
Triangle
Equilateral
Triangle
Two sides are
the same
length.
All three sides
are the same
length.
Practice
Classify each triangle by its angles
and its sides.
1).
Acute and
equilateral
2).
3).
4).
Acute and
isosceles
Obtuse
and
scalene
Right and
scalene
Interior Angles of a Triangle
The sum of the measures of the
interior angles of a triangle is
180°.
°
Practice
Find the missing angle for each triangle.
26° 119
1).
degrees
x 35°
3).
32 degrees
58°
x
2).
𝟑𝟓°
65°
80 degrees
x
Closure
How are triangles
classified?
Triangle
Inequality
Theorem
Triangle Inequality Theorem
Any side of a triangle must be shorter
than the other two sides added
together. If it was longer, the other
two sides would not meet.
Example 1:
triangle?
5 + 4 = 9
Will the following lengths make a
5 cm, 7 cm, 4 cm
9 > 7
yes, this makes a
triangle
Example 2: Will the following lengths
make a triangle?
2 in, 4 in, 6 in
2 + 4 = 6
6= 6
no, this does not
make a triangle
Practice
Tell if the following side lengths will make a triangle.
1). 7 in, 2 in, 4 in
no
2). 8 cm, 10 cm, 12 cm
yes
3). 15 yd, 16 yd, 12 yd 4). 7 ft, 8ft, 9 ft
yes
5). 10 in, 12 in, 22 in
no
yes
6). 5 cm, 8 cm, 4 cm
yes
Closure
What are the possible lengths
for the third side of a triangle
with the following 2 lengths?
5 in and 4 in
2, 3, 4, 5,
6,7,8