Download Classify These Triangles by Sides and Angles

Classify These Triangles by Sides and
Angles
Chapter 4
Congruent Triangles
Section 4.1: Triangle Sum Properties
Todays Objective: Determine if a right
triangle can be an obtuse triangle
and explain why or why not.
Triangle Classifications
By Sides:
• Equilateral Triangle
– All sides have the same
length
By Angles:
• Equiangular Triangle
– All internal angles have
the same measure
Triangle Classifications
What do we call a polygon
that is both equilateral
and equiangular?
Regular Polygon
What is the sum of the
measures of the interior
angles of any triangle?
Theorem 4.1: Triangle Sum Theorem
The sum of the measures of the interior
angles of any triangle is 180°
Triangle Classifications
By Sides:
• Isosceles Triangle
– Two sides have the same
length
By Angles:
• Acute Triangle
– All internal angles are
acute.
Triangle Classifications
By Sides:
• Scalene Triangle
– All sides have different lengths
By Angles:
• Obtuse Triangle
– One internal angle is obtuse
Triangle Classifications
By Sides:
• Scalene or Isosceles
Triangle
– At least one side (the
hypotenuse) must be
longer than the other two.
By Angles:
• Right Triangle
– One internal angle is a
Right Angle (measures 90°)
Angle Measures
The measure of angle d must be equal to what?
𝒎<𝒅=?
Angle d and Angle c are a ___________
𝒎<𝒅=𝒎<𝒂+𝒎<𝒃
b
a
c
d
Theorem 4.2
Exterior Angle Theorem
• The measure of the
exterior angle of a
triangle is equal to the
sum of the measures of
the two nonadjacent
interior angles
Right Triangles
Can a right triangle ever
be an obtuse triangle?
B
𝟗𝟎° + 𝒎 < 𝑨 + 𝒎 < 𝑩 = 𝟏𝟖𝟎°
A
The Acute angles of a Right
Triangle must be
Complementary.
Homework
Section 4.1
p.221
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