Worksheet: Congruence of Polygons

In this worksheet, we will practice identifying congruent polygons and find out about their properties to solve problems.

Q1:

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

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

Q2:

Given that 𝐴 𝐵 𝐶 𝑋 𝑌 𝑍 , find 𝑚 𝐴 .

Q3:

Use the figure to determine 𝑚 𝐷 .

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 𝑅 𝑆 𝑇 𝑀 𝑁 𝑂 , what is 𝑅 𝑇 congruent to?

  • A 𝑁 𝑀
  • B 𝑁 𝑂
  • C 𝑀 𝑂

Q7:

Given that 𝑃 𝑄 𝑅 𝑇 𝑈 𝑉 , which of the following is certain?

  • A 𝑅 𝑇
  • B 𝑃 𝑉
  • C 𝑅 𝑈
  • D 𝑃 𝑇
  • E 𝑄 𝑉

Q8:

If 𝐴 𝐵 𝐶 𝑋 𝑌 𝑍 , what is the length of 𝑋 𝑌 ?

Q9:

In the following figure, 𝐴 𝐶 = 𝐶 𝐷 , 𝐴 𝐵 = 𝐵 𝐷 , 𝑚 𝐴 𝐵 𝐶 = 8 1 , and 𝑚 𝐴 = 4 3 . Find 𝑚 𝐴 𝐶 𝐷 .

  • A 8 6
  • B 1 6 2
  • C 5 6
  • D 1 1 2

Q10:

Given that 𝑋 𝑌 𝐾 𝑀 𝐴 𝐵 𝐶 𝑀 , find the measure of 𝐾 𝑀 𝐶 .

Q11:

Find the values of 𝑥 and 𝑦 .

  • A 𝑥 = 5 . 1 5 c m , 𝑦 = 7 2
  • B 𝑥 = 6 . 3 9 c m , 𝑦 = 7 2
  • C 𝑥 = 5 . 1 5 c m , 𝑦 = 5 0
  • D 𝑥 = 5 . 7 c m , 𝑦 = 5 8

Q12:

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

  • Ano
  • Byes

Q13:

Are any two equilateral triangles congruent?

  • A no
  • B yes

Q14:

Given that 𝑃 𝑄 𝑅 𝑇 𝑈 𝑉 , which of the following is certain?

  • A 𝑄 𝑅 𝑇 𝑈
  • B 𝑃 𝑄 𝑈 𝑉
  • C 𝑄 𝑅 𝑇 𝑉
  • D 𝑃 𝑄 𝑇 𝑈
  • E 𝑃 𝑅 𝑈 𝑉

Q15:

Which of the following congruence statements is true?

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

Q16:

Are the given polygons congruent?

  • Ano
  • Byes

Q17:

Are the polygons shown congruent?

  • Ayes
  • Bno

Q18:

Given that polygons 𝐴 𝐵 𝐶 𝐷 and 𝑋 𝐶 𝐵 𝑌 are congruent, determine the angles at 𝑌 , 𝐴 , and 𝑚 𝐴 𝐵 𝐶 .

  • A 1 1 9 , 9 0 , 7 4
  • B 1 1 9 , 7 7 , 9 0
  • C 9 0 , 7 7 , 7 4
  • D 1 1 9 , 7 7 , 7 4

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