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Worksheet: Applications of Congruence of Polygons

Q1:

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

  • Ayes
  • Bno

Q2:

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

  • A
  • B
  • C
  • D

Q3:

Given that β–³ 𝐴 𝐡 𝐢 β‰… β–³ 𝑋 π‘Œ 𝑍 , find π‘š ∠ 𝐴 .

Q4:

Use the figure to determine .

  • A
  • B
  • C
  • D

Q5:

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

Q6:

Given that , find the size of .

  • A
  • B
  • C
  • D

Q7:

If β–³ 𝐴 𝐡 𝐢 β‰… β–³ 𝑋 π‘Œ 𝑍 , what is the length of 𝑋 π‘Œ ?

Q8:

Given that β–³ 𝑃 𝑄 𝑅 β‰… β–³ 𝑇 π‘ˆ 𝑉 , which of the following is certain?

  • A ∠ 𝑅 β‰… ∠ 𝑇
  • B ∠ 𝑃 β‰… ∠ 𝑉
  • C ∠ 𝑅 β‰… ∠ π‘ˆ
  • D ∠ 𝑃 β‰… ∠ 𝑇
  • E ∠ 𝑄 β‰… ∠ 𝑉

Q9:

Find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 5 . 1 5 c m , 𝑦 = 7 2 ∘
  • B π‘₯ = 6 . 3 9 c m , 𝑦 = 7 2 ∘
  • C π‘₯ = 5 . 1 5 c m , 𝑦 = 5 0 ∘
  • D π‘₯ = 5 . 7 c m , 𝑦 = 5 8 ∘

Q10:

Which of the following congruence statements is true?

  • A
  • B
  • C
  • D

Q11:

If β–³ 𝑅 𝑆 𝑇 β‰… β–³ 𝑀 𝑁 𝑂 , what is 𝑅 𝑇 congruent to?

  • A 𝑁 𝑀
  • B 𝑁 𝑂
  • C 𝑀 𝑂

Q12:

Are the given polygons congruent?

  • Ano
  • Byes

Q13:

Are any two equilateral triangles congruent?

  • A no
  • B yes

Q14:

Are the polygons shown congruent?

  • Ayes
  • Bno

Q15:

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

  • Ano
  • Byes

Q16:

Given that β–³ 𝑃 𝑄 𝑅 β‰… β–³ 𝑇 π‘ˆ 𝑉 , which of the following is certain?

  • A 𝑄 𝑅 β‰… 𝑇 π‘ˆ
  • B 𝑃 𝑄 β‰… π‘ˆ 𝑉
  • C 𝑄 𝑅 β‰… 𝑇 𝑉
  • D 𝑃 𝑄 β‰… 𝑇 π‘ˆ
  • E 𝑃 𝑅 β‰… π‘ˆ 𝑉

Q17:

In the following figure, , , , and . Find .

  • A
  • B
  • C
  • D

Q18:

Given that polygons and are congruent, determine the angles at , , and .

  • A , ,
  • B , ,
  • C , ,
  • D , ,