Triangle Sum Theorem: 4 Proofs

linzi_bullard, Feb 19, 2021

Triangle Angle Sum Theorem Proofs

Table of Contents

  1. Triangle Sum Theorem
    1. Triangle Angle Sum Theorem
  2. Rotation Proof
    1. Proof By Rotation (v1)
    2. Visualizing the Angle Sum in a Triangle
  3. Translation Proof
    1. Proof by Translation
    2. Proof by Translation (v2)
  4. Reflection Proof
    1. Reflection Proof
  5. Parallel Lines Proof
    1. Triangle Sum Theorem

1.

Triangle Sum Theorem

  • 1. Triangle Angle Sum Theorem

1.1.

Triangle Angle Sum Theorem

– Tim Brzezinski

2.

Rotation Proof

  • 1. Proof By Rotation (v1)
  • 2. Visualizing the Angle Sum in a Triangle

2.1.

Proof By Rotation (v1)

– GeoGebra Team German, linzi_bullard, Tim Brzezinski

2.2.

–

3.

Translation Proof

  • 1. Proof by Translation
  • 2. Proof by Translation (v2)

3.1.

Proof by Translation

– linzi_bullard, Tim Brzezinski

3.2.

–

4.

Reflection Proof

  • 1. Reflection Proof

4.1.

Reflection Proof

Animation that the sum of the angles of a triangle is a straight angle; α+β+γ=180°[br]Click and drag the the vertices of the triangle to change the angles!
How did we choose the segment for the reflection of point B? (Hint: Check the box for midpoints.)[br]How did we choose the segments for the reflections of point A and point C?[br]Which pairs of triangles are congruent (equal)?[br]How does this animation show that the sum of the angles of any triangle is 180°?
– linzi_bullard, Erdenesuvd, Linda Fahlberg-Stojanovska

5.

Parallel Lines Proof

  • 1. Triangle Sum Theorem

5.1.

Triangle Sum Theorem

The applet proves the triangle sum theorem.
Move the blue points to change the shape of the triangle.
– Breck Jacobs

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