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?

  • A𝐴𝐵𝐶𝐷𝐴𝐶
  • B𝐵𝐶𝐴𝐷𝐴𝐶
  • C𝐴𝐵𝐶𝐶𝐴𝐷
  • D𝐴𝐶𝐵𝐷𝐴𝐶

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?

  • A𝑀𝑂
  • B𝑁𝑂
  • C𝑁𝑀

Q7:

Given that 𝑃𝑄𝑅𝑇𝑈𝑉, which of the following is certain?

  • A𝑄𝑉
  • B𝑅𝑇
  • C𝑅𝑈
  • D𝑃𝑇
  • E𝑃𝑉

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.

  • A112
  • B86
  • C56
  • D162

Q10:

Given that 𝑋𝑌𝐾𝑀𝐴𝐵𝐶𝑀, find the measure of 𝐾𝑀𝐶.

Q11:

Find the values of 𝑥 and 𝑦.

  • A𝑥=6.39cm, 𝑦=72
  • B𝑥=5.7cm, 𝑦=58
  • C𝑥=5.15cm, 𝑦=72
  • D𝑥=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 𝑃𝑄𝑅𝑇𝑈𝑉, which of the following is certain?

  • A𝑃𝑅𝑈𝑉
  • B𝑄𝑅𝑇𝑈
  • C𝑃𝑄𝑇𝑈
  • D𝑄𝑅𝑇𝑉
  • E𝑃𝑄𝑈𝑉

Q15:

Which of the following congruence statements is true?

  • A𝐴𝐷𝐵𝐶𝐷𝐴
  • B𝐴𝐵𝐷𝐴𝐶𝐷
  • C𝐴𝐵𝐷𝐶𝐷𝐴
  • D𝐴𝐵𝐷𝐴𝐷𝐶

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.

  • 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 𝐴𝐵𝐶𝐷.

Q20:

If 𝐿𝑀𝑁𝑄𝑅𝑆, find the values of 𝑥 and 𝑦.

  • A𝑥=5, 𝑦=11
  • B𝑥=4.4, 𝑦=11
  • C𝑥=5, 𝑦=3.7
  • D𝑥=4.4, 𝑦=3.7
  • E𝑥=35, 𝑦=5.5

Q21:

If 𝐴𝐵𝐶𝐷𝐹𝐸, find the values of 𝑥 and 𝑦.

  • A𝑥=35.6, 𝑦=9.2
  • B𝑥=71.6, 𝑦=17.6
  • C𝑥=34, 𝑦=20
  • D𝑥=18.8, 𝑦=17.6
  • E𝑥=94, 𝑦=20

Q22:

Find 𝑆𝑊 in the given figure.

Q23:

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

  • A𝑥=3117, 𝑦=6217
  • B𝑥=4, 𝑦=12
  • C𝑥=8, 𝑦=4
  • D𝑥=17104, 𝑦=17208
  • E𝑥=5919, 𝑦=1917

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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