Lesson Worksheet: Congruent Polygons Mathematics • 8th Grade

In this worksheet, we will practice identifying congruent polygons and using their properties to find a missing side length or angle.

Q1:

The symbol β‰… means that the two objects are congruent. Which statement is true?

  • A△𝐴𝐡𝐢≅△𝐷𝐴𝐢
  • B△𝐡𝐢𝐴≅△𝐷𝐴𝐢
  • C△𝐴𝐡𝐢≅△𝐢𝐴𝐷
  • D△𝐴𝐢𝐡≅△𝐷𝐴𝐢

Q2:

Given that β–³π΄π΅πΆβ‰…β–³π‘‹π‘Œπ‘, find π‘šβˆ π΄.

Q3:

Use the figure to determine π‘šβˆ π·.

Q4:

Are two squares congruent if the side length of one square is equal to the side length of the other?

  • AYes
  • BNo

Q5:

Two squares are congruent. If one has side length 78, what is the side length of the other?

Q6:

If △𝑅𝑆𝑇≅△𝑀𝑁𝑂, what is 𝑅𝑇 congruent to?

  • A𝑀𝑂
  • B𝑁𝑂
  • C𝑁𝑀

Q7:

Given that β–³π‘ƒπ‘„π‘…β‰…β–³π‘‡π‘ˆπ‘‰, which of the following is certain?

  • Aβˆ π‘„β‰…βˆ π‘‰
  • Bβˆ π‘…β‰…βˆ π‘‡
  • Cβˆ π‘…β‰…βˆ π‘ˆ
  • Dβˆ π‘ƒβ‰…βˆ π‘‡
  • Eβˆ π‘ƒβ‰…βˆ π‘‰

Q8:

If β–³π΄π΅πΆβ‰…β–³π‘‹π‘Œπ‘, what is the length of π‘‹π‘Œ?

Q9:

In the following figure, 𝐴𝐢=𝐢𝐷, 𝐴𝐡=𝐡𝐷, π‘šβˆ π΄π΅πΆ=81∘, and π‘šβˆ π΄=43∘. Find π‘šβˆ π΄πΆπ·.

  • A112∘
  • B86∘
  • C56∘
  • D162∘

Q10:

Given that π‘‹π‘ŒπΎπ‘€β‰…π΄π΅πΆπ‘€, find the measure of βˆ πΎπ‘€πΆ.

Q11:

Find the values of π‘₯ and 𝑦.

  • Aπ‘₯=6.39cm, 𝑦=72∘
  • Bπ‘₯=5.7cm, 𝑦=58∘
  • Cπ‘₯=5.15cm, 𝑦=72∘
  • Dπ‘₯=5.15cm, 𝑦=50∘

Q12:

Are two polygons congruent if their corresponding sides have the same length?

  • AYes
  • BNo

Q13:

Are any two equilateral triangles congruent?

  • AYes
  • BNo

Q14:

Given that β–³π‘ƒπ‘„π‘…β‰…β–³π‘‡π‘ˆπ‘‰, which of the following is certain?

  • Aπ‘ƒπ‘…β‰…π‘ˆπ‘‰
  • Bπ‘„π‘…β‰…π‘‡π‘ˆ
  • Cπ‘ƒπ‘„β‰…π‘‡π‘ˆ
  • D𝑄𝑅≅𝑇𝑉
  • Eπ‘ƒπ‘„β‰…π‘ˆπ‘‰

Q15:

Which of the following congruence statements is true?

  • A△𝐴𝐷𝐡≅△𝐢𝐷𝐴
  • B△𝐴𝐡𝐷≅△𝐴𝐢𝐷
  • C△𝐴𝐡𝐷≅△𝐢𝐷𝐴
  • D△𝐴𝐡𝐷≅△𝐴𝐷𝐢

Q16:

Are the given polygons congruent?

  • AYes
  • BNo

Q17:

Are the polygons shown congruent?

  • ANo
  • BYes

Q18:

Given that polygons 𝐴𝐡𝐢𝐷 and π‘‹πΆπ΅π‘Œ are congruent, determine the angles at π‘Œ, 𝐴, and π‘šβˆ π΄π΅πΆ.

  • A119∘, 77∘, 74∘
  • B90∘, 77∘,74∘
  • C119∘, 90∘,74∘
  • D119∘, 77∘, 90∘

Q19:

The two quadrilaterals in the given figure are congruent. Work out the perimeter of 𝐴𝐡𝐢𝐷.

Q20:

If △𝐿𝑀𝑁≅△𝑄𝑅𝑆, find the values of π‘₯ and 𝑦.

  • Aπ‘₯=5, 𝑦=11
  • Bπ‘₯=4.4, 𝑦=11
  • Cπ‘₯=5, 𝑦=3.7
  • Dπ‘₯=4.4, 𝑦=3.7
  • Eπ‘₯=35, 𝑦=5.5

Q21:

If △𝐴𝐡𝐢≅△𝐷𝐹𝐸, find the values of π‘₯ and 𝑦.

  • Aπ‘₯=35.6, 𝑦=9.2
  • Bπ‘₯=71.6, 𝑦=17.6
  • Cπ‘₯=34, 𝑦=20
  • Dπ‘₯=18.8, 𝑦=17.6
  • Eπ‘₯=94, 𝑦=20

Q22:

Find π‘†π‘Š in the given figure.

Q23:

Given that △𝑃𝑄𝑆≅△𝑅𝑄𝑆, find the values of π‘₯ and 𝑦.

  • Aπ‘₯=3117, 𝑦=6217
  • Bπ‘₯=4, 𝑦=12
  • Cπ‘₯=8, 𝑦=4
  • Dπ‘₯=17104, 𝑦=17208
  • Eπ‘₯=5919, 𝑦=1917

Q24:

Given that β–³π΄π΅πΆβ‰…β–³π‘‹π‘Œπ‘, find π‘šβˆ πΆ.

Q25:

The perimeter of the polygon 𝐴𝐡𝐢𝐷𝐸 is 176 cm and 𝐴𝐡𝐢𝐷𝐸≅𝐹𝑀𝐿𝐷𝐸. Given that πΈβˆˆβƒ–οƒ©οƒ©οƒ©οƒ©βƒ—π΄πΉ and 𝐷𝐸=48cm, find the perimeter of the figure 𝐴𝐡𝐢𝐷𝐿𝑀𝐹.

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