Triangle angle-sum property

Definition of Triangle Angle-Sum Property:

• The sum of the three interior angles of any triangle is always 180 degrees.
• Mathematically:

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Types of Triangles:

• Acute Triangle: All three angles are less than 90°.
• Right Triangle: One angle is exactly 90°.
• Obtuse Triangle: One angle is greater than 90°.

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Proof of the Triangle Angle-Sum Property:

• Consider a triangle ABC.
  Extend one side, say BC.
  Draw a line parallel to BC through the opposite vertex A.
  The alternate interior angles formed at the vertex will show that the sum of the angles of the triangle is 180°.

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Application of Triangle Angle-Sum Property:

• Finding Missing Angles:
  If two angles of a triangle are known, the third angle can be easily found using the property.

Example:

• Verification of Angle Measures:
  If the sum of the angles in a triangle does not add up to 180°, then the figure is not a triangle.

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Importance in Geometric Constructions:

• This property helps in the construction of triangles when the sum of the angles is given.

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Corollary – Exterior Angle Theorem:

• The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
  Example:

If an exterior angle ∠D is formed by extending side BC of triangle ABC, then:
∠D=∠A+∠B.

Learn with an example

Let’s practice!