Worksheet: Similar and Congruent Figures

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

Q1:

Which two of these triangles are similar?

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

Q2:

Complete the sentence: These figures are .

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

Q3:

Complete the sentence: These figures are .

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

Q4:

Complete the sentence: These figures are .

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

Q5:

Which two figures are congruent?

  • Ab and c
  • Ba and b
  • Ca and c

Q6:

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

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

Q7:

If two triangles are similar and, additionally, the ratio between the lengths of two corresponding sides is 11, what can you say about the triangles?

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

Q8:

Consider two congruent rectangles 𝐴𝐵𝐶𝐷 and 𝑋𝑌𝑍𝐿. Which line in 𝑋𝑌𝑍𝐿 corresponds to 𝐴𝐵?

  • A 𝑋 𝐿
  • B 𝑋 𝑌
  • C 𝑌 𝑍

Q9:

Given that triangles 𝐴𝐵𝐶 and 𝐸𝐷𝐶 are similar, determine the value of 𝑥.

Q10:

Noah 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 .

  • Aequal
  • Bnot proportional
  • Cproportional
  • Dcongruent

Q12:

Complete the sentence: These figures are .

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

Q13:

Which two shapes are congruent?

  • Aa and b
  • Bb and c
  • Ca 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 =413in, height =413in
  • Bbase length =416in, height =413in
  • Cbase length =413in, height =414in
  • Dbase length =414in, height =416in
  • Ebase length =413in, height =416in

Q15:

Complete the sentence: These figures are .

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

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