Lesson Worksheet: Angle-Angle Triangle Similarity Mathematics

In this worksheet, we will practice determining whether two triangles are similar using the equality of corresponding angles (Angle-Angle criteria) and using the similarity to find unknown angles.


Find the length of 𝐵𝐷.


The figure shows triangle 𝐴𝐵𝐶.

Work out the value of 𝑥.

Work out the value of 𝑦.

Work out the perimeter of 𝐴𝐵𝐶.


In the given figure, 𝐺 lies on both 𝐸𝐻 and 𝐷𝐹. 𝐴𝐵 and 𝐷𝐻 each have a length of 4, and 𝐺𝐷 has a length of 3.

Calculate the length of 𝐴𝐶.

  • A143
  • B5
  • C4
  • D3
  • E163

Calculate the length of 𝐹𝐺.

Hence, calculate the length of 𝐸𝐹.

  • A43
  • B1
  • C34
  • D3
  • E4


Determine the length of 𝐴𝐶.


If 𝐸𝐷=4.3cm, find the length of 𝐴𝐶.


In the two triangles shown, 𝑚𝐷𝐹𝐸=30 and 𝑚𝐷𝐸𝐹=42. What is 𝑚𝐴?


What does the AA criterion for triangles allow us to prove?

  • AIf two corresponding angles in two triangles have equal measures, then they must be similar.
  • BIf the corresponding sides of two triangles are proportional, then the two triangles are similar.
  • CIf, in the two triangles, one pair of corresponding sides are proportional and the included angles are equal, then the two triangles are similar.
  • DIf a corresponding side and angle are equal in two triangles, then the two triangles are similar.
  • EIf the corresponding sides of two triangles are equal, then the two triangles are congruent.


Find the length of 𝐽𝐾.


Triangles 𝐴𝐷𝐸 and 𝐴𝐵𝐶 in the given figure are similar. What, if anything, must be true of the lines 𝐷𝐸 and 𝐵𝐶?

  • AThey are parallel.
  • BThey are perpendicular.


In the given figure, 𝐴𝐵 and 𝐷𝐸 are parallel. Using the AA criterion, what can we say about triangles 𝐴𝐵𝐶 and 𝐷𝐸𝐶?

  • AThey are congruent.
  • BThey are neither similar nor congruent.
  • CThey are isosceles triangles.
  • DThey are similar.
  • EThey are equilateral triangles.

This lesson includes 64 additional questions and 315 additional question variations for subscribers.

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