Angles Inside the Triangle 4-1A

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Angles Inside the Triangle 4-1A

• What is a triangle?
• What is the sum of the measures of the interior
  of any triangle?
• How are triangles classified and named?

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Definition

• A triangle is a figure formed by three line
  segments that connect three noncollinear points.

vertex
C
Side
Side
A
B
Side
vertex
vertex
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Naming a triangle

• A triangle is named using its vertices and a ?
  symbol. This triangle can be named ? ABC

C
A
B
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The Three Angles

1. Number the angles of your triangle.
2. Cut off each angle of your triangle.
3. Arrange your vertices (with the numbers)
   together.
4. What do you notice?

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Try It

• Two angles of a triangle measure 40 and 58.
  What is the measure of the third angle?

82
?
40
58
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Triangle Classification by Sides
E
B
H
A
C
G
I

• Scalene
• no sides congruent.

Equilateral All sides congruent.
D
F
Isosceles two sides congruent.
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Special Names for Isosceles Triangles
C
Vertex
Vertex angle

• Leg

Leg
Base
A
B
Base angles
Base Angles
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Triangle Classification by Angles

• Acute
• All angles
• are acute.

Right Has one right angle.
Obtuse Has one obtuse angle.
Equiangular All angles are equal.
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Special Names for Right Triangles
F
Hypotenuse
Leg
D
E
Leg
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Try ItClassify each triangle using both angle
and side classification.
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Try It
Draw an isosceles triangle, ? PRS, with base PR.
Name the legs and the vertex angle. Draw a right
triangle, ?FGH, with right angle F. Name the
hypotenuse and the legs.
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Triangle Angle-Sum Theorem
The sum of the measures of the angles of a
triangle is 180
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• What is a triangle?
• A figure formed by three line segments that
  connect three noncollinear points.
• What is the sum of the measures of the interior
  of any triangle?
• The sum of the measures of the angles of a
  triangle is 180
• How are triangles classified and named?
• Triangles are classified by sides and angles.
• Sides scalene, isosceles and equilateral.
• Angles acute, obtuse, right and equiangular.

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Assignment 4-1A

• Page 245, 1-8, 10-14, 25-30