Worksheet: Congruent Polygons

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

Q1:

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

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

Q2:

Given that 𝐴𝐵𝐶𝑋𝑌𝑍, find 𝑚𝐴.

Q3:

Use the figure to determine 𝑚𝐷.

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 𝑅𝑆𝑇𝑀𝑁𝑂, what is 𝑅𝑇 congruent to?

  • A 𝑀 𝑂
  • B 𝑁 𝑂
  • C 𝑁 𝑀

Q7:

Given that 𝑃𝑄𝑅𝑇𝑈𝑉, which of the following is certain?

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

Q8:

If 𝐴𝐵𝐶𝑋𝑌𝑍, what is the length of 𝑋𝑌?

Q9:

In the following figure, 𝐴𝐶=𝐶𝐷, 𝐴𝐵=𝐵𝐷, 𝑚𝐴𝐵𝐶=81, and 𝑚𝐴=43. Find 𝑚𝐴𝐶𝐷.

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

Q10:

Given that 𝑋𝑌𝐾𝑀𝐴𝐵𝐶𝑀, find the measure of 𝐾𝑀𝐶.

Q11:

Find the values of 𝑥 and 𝑦.

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

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 𝑃𝑄𝑅𝑇𝑈𝑉, which of the following is certain?

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

Q15:

Which of the following congruence statements is true?

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

Q16:

Are the given polygons congruent?

  • Ayes
  • Bno

Q17:

Are the polygons shown congruent?

  • Ano
  • Byes

Q18:

Given that polygons 𝐴𝐵𝐶𝐷 and 𝑋𝐶𝐵𝑌 are congruent, determine the angles at 𝑌, 𝐴, and 𝑚𝐴𝐵𝐶.

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

Q19:

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

Q20:

If 𝐿𝑀𝑁𝑄𝑅𝑆, find the values of 𝑥 and 𝑦.

  • A 𝑥 = 5 , 𝑦 = 1 1
  • B 𝑥 = 4 . 4 , 𝑦 = 1 1
  • C 𝑥 = 5 , 𝑦 = 3 . 7
  • D 𝑥 = 4 . 4 , 𝑦 = 3 . 7
  • E 𝑥 = 3 5 , 𝑦 = 5 . 5

Q21:

If 𝐴𝐵𝐶𝐷𝐹𝐸, find the values of 𝑥 and 𝑦.

  • A 𝑥 = 3 5 . 6 , 𝑦 = 9 . 2
  • B 𝑥 = 7 1 . 6 , 𝑦 = 1 7 . 6
  • C 𝑥 = 3 4 , 𝑦 = 2 0
  • D 𝑥 = 1 8 . 8 , 𝑦 = 1 7 . 6
  • E 𝑥 = 9 4 , 𝑦 = 2 0

Q22:

Find 𝑆𝑊 in the given figure.

Q23:

Given that 𝑃𝑄𝑆𝑅𝑄𝑆, find the values of 𝑥 and 𝑦.

  • A 𝑥 = 3 1 1 7 , 𝑦 = 6 2 1 7
  • B 𝑥 = 4 , 𝑦 = 1 2
  • C 𝑥 = 8 , 𝑦 = 4
  • D 𝑥 = 1 7 1 0 4 , 𝑦 = 1 7 2 0 8
  • E 𝑥 = 5 9 1 9 , 𝑦 = 1 9 1 7

Q24:

Given that 𝐴𝐵𝐶𝑋𝑌𝑍, find 𝑚𝐶.

Q25:

The perimeter of the polygon 𝐴𝐵𝐶𝐷𝐸 is 176 cm and 𝐴𝐵𝐶𝐷𝐸𝐹𝑀𝐿𝐷𝐸. Given that 𝐸𝐴𝐹 and 𝐷𝐸=48cm, find the perimeter of the figure 𝐴𝐵𝐶𝐷𝐿𝑀𝐹.

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