Angle Bisector Theorem: Proof and Example


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question 1 of 3

Which of the following represents the angle bisector theorem for the pictured triangle?

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1. In the pictured triangle, FE is an angle bisector. What is the length of GE?

2. In the pictured triangle, XV is an angle bisector. What is the length of XY?

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About This Quiz & Worksheet

These assessments test not only your understanding of the angle bisector theorem, but also your ability to apply the theorem by solving for the values of proportional sides. In order to succeed, you will need to be familiar with solving proportions problems.

Quiz & Worksheet Goals

To pass this quiz, you will need to:

  • Identify similar triangles created by an angle bisector
  • Determine the relationship between the sides of similar triangles
  • Solve proportions problems to find the length of a triangle side

Skills Practiced

  • Interpreting information - Verify that you can follow the logic of the angle bisector theorem proof and interpret it correctly
  • Knowledge application - Use your knowledge to figure out the relationship between the similar triangles (which sides are proportional)
  • Problem solving - Apply your understanding of the angle bisector theorem by solving for unknown values in practice problems
  • Making connections - Relate prior knowledge about proportions problems to put the theorem to use

Additional Learning

To really understand how this theorem can really be true, review the lesson Angle Bisector Theorem: Proof and Example. The lesson covers the following objectives:

  • Construct additional structures on a geometrical shape in order to facilitate a proof
  • Identify alternate anterior angles in a construction
  • Verify the congruence of alternate interior angles
  • Describe the properties of isosceles triangles