Lesson Worksheet: Similar and Congruent Figures Mathematics • 8th Grade

In this worksheet, we will practice determining whether two given figures are similar or congruent.


Which two of these triangles are similar?

  • A(2), (3)
  • B(1), (3)
  • C(2), (4)
  • D(1), (4)


Complete the sentence: These figures are .

  • Asimilar but not congruent
  • Bcongruent
  • Cneither similar nor congruent


Complete the sentence: These figures are .

  • Aneither similar nor congruent
  • Bsimilar but not congruent
  • Ccongruent


Complete the sentence: These figures are .

  • Aneither similar nor congruent
  • Bcongruent
  • Csimilar but not congruent


Which two figures are congruent?

  • A(b) and (c)
  • B(a) and (b)
  • C(a) and (c)


Consider three polygons: 𝐴, 𝐡, and 𝐢. If 𝐴 and 𝐡 are both similar to 𝐢, what can you say about polygons 𝐴 and 𝐡?

  • AThey are similar.
  • BThey are not congruent.
  • CThey are not similar.
  • DThey must be congruent.


If two triangles are similar and, additionally, the ratio between the lengths of two corresponding sides is 1∢1, what can you say about the triangles?

  • AThey are congruent.
  • BThey have different areas.
  • CThey are not congruent.


Consider two congruent rectangles 𝐴𝐡𝐢𝐷 and π‘‹π‘Œπ‘πΏ. Which line in π‘‹π‘Œπ‘πΏ corresponds to 𝐴𝐡?

  • A𝑋𝐿
  • Bπ‘‹π‘Œ
  • Cπ‘Œπ‘


Given that triangles 𝐴𝐡𝐢 and 𝐸𝐷𝐢 are similar, determine the value of π‘₯.


Anthony has a picture frame that is 18 by 24 inches. If he has another frame congruent to the first one, and one of its sides is 24 inches long, determine the length of the other side.

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