Worksheet: Application of Congruence of Polygons

In this worksheet, we will practice using congruence of polygons to find a missing angle measure or side length.

Q1:

Find 𝑆 𝑊 in the given figure.

Q2:

If 𝐿 𝑀 𝑁 𝑄 𝑅 𝑆 , find the values of 𝑥 and 𝑦 .

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

Q3:

Complete the sentence: These figures are .

  • Aneither similar nor congruent
  • Bsimilar but not congruent
  • Ccongruent

Q4:

The two quadrilaterals in the given figure are congruent. Work out the perimeter of 𝐴 𝐵 𝐶 𝐷 .

Q5:

If 𝐴 𝐵 𝐶 𝐷 𝐹 𝐸 , find the values of 𝑥 and 𝑦 .

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

Q6:

Given that the two polygons shown are congruent, find the length of 𝐿 𝑀 .

Q7:

In the figure, 𝐴 𝐷 𝐸 is congruent to 𝐶 𝐵 𝐹 . Given that 𝑚 𝐹 𝐵 𝐶 = 2 3 and 𝑚 𝐷 𝐴 𝐶 = 6 8 , find 𝑚 𝐷 𝐸 𝐶 .

Q8:

Given that the polygons 𝐴 𝐵 𝐶 𝐷 and 𝐸 𝐹 𝐺 𝐻 are congruent, find the perimeter of the polygon 𝐴 𝐵 𝐶 𝐷 and then 𝑚 𝐹 .

  • A 72 cm, 5 4
  • B 352 cm, 1 0 6
  • C 55 cm, 9 0
  • D 72 cm, 9 0

Q9:

In the figure pentagon is congruent to pentagon .

Work out the length of .

  • A5
  • B2.2
  • C5.8
  • D3.2
  • E81.9

Work out the length of .

  • A2.2
  • B5.8
  • C5
  • D3.2
  • E59

Work out the length of .

  • A81.9
  • B3.2
  • C5
  • D2.2
  • E5.8

Work out the size of angle .

  • A
  • B
  • C
  • D
  • E

Work out the size of angle .

  • A
  • B
  • C
  • D
  • E

Q10:

In the given figure, 𝐴 𝐵 and 𝐷 𝐸 are parallel and 𝐶 lies on both 𝐵 𝐷 and 𝐴 𝐸 .

Work out the value of 𝑥 .

Are triangles 𝐴 𝐵 𝐶 and 𝐸 𝐷 𝐶 congruent?

  • Ayes
  • Bno

Q11:

Find the values of 𝑥 and 𝑦 .

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

Q12:

In the following figure, find the length of 𝑅 𝑇 .

Q13:

Given that 𝑃 𝑄 𝑆 𝑅 𝑄 𝑆 , find the values of 𝑥 and 𝑦 .

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

Q14:

𝐴 𝐵 𝐶 𝐷 𝑀 𝐹 𝐸 𝐷 and 𝐶 is the midpoint of 𝑀 𝐷 . Given that 𝑀 𝐶 = 3 8 . 1 c m , find the length of 𝐴 𝐸 .

Q15:

If 𝐴 is congruent to 𝐵 and 𝑚 𝐴 = 8 1 , what is 𝑚 𝐵 ?

Q16:

Consider two congruent triangles: 𝐷 𝐸 𝐹 and 𝑂 𝑃 𝑄 . Which angle in 𝑂 𝑃 𝑄 corresponds to 𝐸 ?

  • A 𝑄
  • B 𝑂
  • C 𝑃

Q17:

Given that the dashed line is a line of symmetry of 𝑀 𝑁 𝑂 𝑃 , which angle has the same size as 𝑁 𝑂 𝑃 ?

  • A 𝑀 𝑁 𝑃
  • B 𝑀 𝑃 𝑁
  • C 𝑀 𝑃 𝑂
  • D 𝑁 𝑀 𝑃

Q18:

Given that 𝐴 𝐵 𝐶 is congruent to 𝑋 𝑌 𝑍 , 𝑚 𝑋 = 3 4 , and 𝑚 𝑌 = 𝑚 𝑍 , find 𝑚 𝐵 .

Q19:

Consider two congruent polygons 𝐴 𝐵 𝐶 𝐷 and 𝑋 𝑌 𝑍 𝐿 . First, write the line segment in 𝑋 𝑌 𝑍 𝐿 that corresponds to 𝐷 𝐴 . Then, find the angle in 𝑋 𝑌 𝑍 𝐿 whose measure is the same as 𝑚 𝐵 𝐶 𝐷 .

  • A 𝑌 𝑍 , 𝐿 𝑋 𝑌
  • B 𝑋 𝑌 , 𝑍 𝐿 𝑋
  • C 𝑍 𝐿 , 𝑋 𝑌 𝑍
  • D 𝐿 𝑋 , 𝑌 𝑍 𝐿

Q20:

What is the condition for two angles to be congruent?

  • Adifferent in measure
  • Bequal in length
  • Cdifferent in length
  • Dequal in measure

Q21:

The perimeter of the polygon 𝐴 𝐵 𝐶 𝐷 𝐸 is 176 cm and 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 𝑀 𝐿 𝐷 𝐸 . Given that 𝐸 𝐴 𝐹 and 𝐷 𝐸 = 4 8 c m , find the perimeter of the figure 𝐴 𝐵 𝐶 𝐷 𝐿 𝑀 𝐹 .

Q22:

If the polygon 𝐴 𝐵 𝐶 𝐷 𝑀 𝐿 the polygon 𝐾 𝑍 𝑌 𝑋 𝑀 𝐿 , 𝐴 𝐵 = 8 . 3 cm, and 𝐵 𝐶 = 6 cm, find the perimeter of the polygon 𝑀 𝑋 𝑌 𝑍 𝐾 𝐿 .

Q23:

Given that 𝐴 𝐵 𝐶 𝑋 𝑌 𝑍 , find the length of 𝑋 𝑌 and calculate the perimeter of 𝑋 𝑌 𝑍 .

  • A 𝑋 𝑌 = 2 5 c m , the perimeter = 5 7 c m
  • B 𝑋 𝑌 = 7 c m , the perimeter = 3 9 c m
  • C 𝑋 𝑌 = 2 2 c m , the perimeter = 5 4 c m

Q24:

In a test, you are shown two congruent squares. One square has a side length of 6. What is the perimeter of the other?

Q25:

In the following figure, 𝐴 𝐵 𝐵 𝐴 , 𝐵 𝐵 𝐶 𝐶 , and 𝐴 𝐶 𝐶 𝐴 are three congruent and intersecting rectangles. Find 𝑚 𝐵 𝐷 𝐵 .

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.