Worksheet: Similarity and Congruence of Figures

In this worksheet, we will practice differentiating between similar and congruent two-dimensional figures.

Q1:

Which two of these triangles are similar?

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

Q2:

Complete the sentence: These figures are .

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

Q3:

Complete the sentence: These figures are .

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

Q4:

Complete the sentence: These figures are .

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

Q5:

Which two figures are congruent?

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

Q6:

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

Q7:

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

Q8:

Consider two congruent rectangles 𝐴 𝐡 𝐢 𝐷 and 𝑋 π‘Œ 𝑍 𝐿 . Which line in 𝑋 π‘Œ 𝑍 𝐿 corresponds to 𝐴 𝐡 ?

  • A 𝑋 𝐿
  • B π‘Œ 𝑍
  • C 𝑋 π‘Œ

Q9:

Given that triangles 𝐴 𝐡 𝐢 and 𝐸 𝐷 𝐢 are similar, determine the value of π‘₯ .

Q10:

Adel 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.

Q11:

Any two triangles are similar if the lengths of their corresponding sides are .

  • Acongruent
  • Bequal
  • Cnot proportional
  • Dproportional

Q12:

Complete the sentence: These figures are .

  • Acongruent
  • Bsimilar but not congruent
  • Cneither similar nor congruent

Q13:

Which two shapes are congruent?

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

Q14:

Given that all the triangles in this pattern are congruent, find the length of the base of a blue triangle and then determine its height.

  • Abase length = 4 1 3 i n , height = 4 1 4 i n
  • Bbase length = 4 1 6 i n , height = 4 1 3 i n
  • Cbase length = 4 1 4 i n , height = 4 1 6 i n
  • Dbase length = 4 1 3 i n , height = 4 1 6 i n
  • Ebase length = 4 1 3 i n , height = 4 1 3 i n

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