Lesson Worksheet: Similarity of Triangles Mathematics • 8th Grade

In this worksheet, we will practice determining and proving whether two triangles are similar using equality of corresponding angles or proportionality of corresponding sides and practice using similarity to find unknown lengths and angles.

Q1:

Is triangle 𝑀𝑁𝐿 similar to triangle π‘‹π‘π‘Œ?

  • ANo
  • BYes

Q2:

Which of the following triangles is similar to the one seen in the given figure?

  • A
  • B
  • C
  • D
  • E

Q3:

Given that 𝐴𝐡 and 𝐷𝐢 are parallel, are triangles 𝐸𝐢𝐷 and 𝐸𝐴𝐡 similar? If yes, why?

  • ANo
  • BYes, as the side lengths are equal.
  • CYes, as all the corresponding angles in each triangle have equal measures.

Q4:

Are the two triangles in the figure similar?

  • ANo
  • BYes

Q5:

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

  • AThey are parallel.
  • BThey are perpendicular.

Q6:

Which two of these triangles are similar?

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

Q7:

Given that π‘šβˆ πΈπ΄π·=80∘, what is π‘šβˆ πΆπ΅πΈ?

Q8:

Determine the length of 𝐴𝐢.

Q9:

𝐴𝐡𝐢𝐷 is a rectangle in which 𝐴𝐷=21cm, 𝐴𝑋=9cm, and 𝑋𝑀=12cm. Calculate the perimeter of β–³π‘Œπ‘€πΆ.

Q10:

Find the length of 𝐷𝐡 rounded to the nearest hundredth, if needed.

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