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.

Q1:

Find the length of 𝐵𝐷.

Q2:

The figure shows triangle 𝐴𝐵𝐶.

Work out the value of 𝑥.

Work out the value of 𝑦.

Work out the perimeter of 𝐴𝐵𝐶.

Q3:

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

Q4:

Determine the length of 𝐴𝐶.

Q5:

If 𝐸𝐷=4.3cm, find the length of 𝐴𝐶.

Q6:

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

Q7:

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.

Q8:

Find the length of 𝐽𝐾.

Q9:

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.

Q10:

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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