Worksheet: Application of Lines of Symmetry

In this worksheet, we will practice finding a missing angle measure or a missing side length in one of two congruent figures.

Q1:

Given that 𝑋 𝑌 is the line of symmetry of the polygon 𝐴 𝐵 𝑌 𝐶 𝐷 , determine the perimeter of 𝐴 𝐵 𝑌 𝐶 𝐷 .

Q2:

In the figure, 𝐷 𝐵 𝐶 is symmetrical about line 𝐿 . If 𝑚 𝐶 = 6 9 , what is 𝑚 𝐴 𝐵 𝐷 ?

Q3:

In the figure, 𝐴 , 𝐹 , and 𝐵 are collinear, with 𝐴 𝐵 = 1 0 . If 𝐹 𝐷 is a line of symmetry of polygon 𝐴 𝐵 𝐶 𝐷 𝐸 , find 𝑚 𝐶 𝐷 𝐸 and the length 𝐵 𝐹 .

  • A 𝑚 𝐶 𝐷 𝐸 = 6 8 , 𝐵 𝐹 = 1 0
  • B 𝑚 𝐶 𝐷 𝐸 = 6 8 , 𝐵 𝐹 = 5
  • C 𝑚 𝐶 𝐷 𝐸 = 1 3 6 , 𝐵 𝐹 = 1 0
  • D 𝑚 𝐶 𝐷 𝐸 = 1 3 6 , 𝐵 𝐹 = 5

Q4:

Two of a triangle’s sides are 16 and 2. If the triangle has one line of symmetry, what is its perimeter?

Q5:

Given that 𝐿 is a line of symmetry for the shape 𝐴 𝐵 𝐶 𝐷 𝐸 , calculate 𝑚 𝐵 𝐶 𝐷 .

Q6:

Segment 𝐶 𝐷 has mirror symmetry in line 𝐴 𝐹 . Given that 𝐸 𝐷 = 5 and 𝐵 𝐶 = 5 . 1 , calculate the perimeters of 𝐴 𝐶 𝐹 𝐷 and 𝐵 𝐶 𝐷 .

  • Aperimeter of 𝐴 𝐶 𝐹 𝐷 = 2 5 , perimeter of 𝐵 𝐶 𝐷 = 1 5 . 2
  • Bperimeter of 𝐴 𝐶 𝐹 𝐷 = 1 4 . 9 , perimeter of 𝐵 𝐶 𝐷 = 1 0 . 1
  • Cperimeter of 𝐴 𝐶 𝐹 𝐷 = 2 9 . 8 , perimeter of 𝐵 𝐶 𝐷 = 2 6 . 6
  • Dperimeter of 𝐴 𝐶 𝐹 𝐷 = 2 9 . 8 , perimeter of 𝐵 𝐶 𝐷 = 2 0 . 2

Q7:

Given that 𝐿 is a line of symmetry for the shape 𝐴 𝐵 𝐶 𝐷 𝐸 , calculate 𝑚 𝐵 𝐶 𝐷 .

Q8:

In the figure, 𝐴 , 𝐹 , and 𝐵 are collinear, with 𝐴 𝐵 = 1 4 . If 𝐹 𝐷 is a line of symmetry of polygon 𝐴 𝐵 𝐶 𝐷 𝐸 , find 𝑚 𝐶 𝐷 𝐸 and the length 𝐵 𝐹 .

  • A 𝑚 𝐶 𝐷 𝐸 = 6 9 , 𝐵 𝐹 = 1 4
  • B 𝑚 𝐶 𝐷 𝐸 = 6 9 , 𝐵 𝐹 = 7
  • C 𝑚 𝐶 𝐷 𝐸 = 1 3 8 , 𝐵 𝐹 = 1 4
  • D 𝑚 𝐶 𝐷 𝐸 = 1 3 8 , 𝐵 𝐹 = 7

Q9:

Two of a triangle’s sides are 18 and 7. If the triangle has one line of symmetry, what is its perimeter?

Q10:

Given that 𝑋 𝑌 is the line of symmetry of the polygon 𝐴 𝐵 𝑌 𝐶 𝐷 , determine the perimeter of 𝐴 𝐵 𝑌 𝐶 𝐷 .

Q11:

Segment 𝐶 𝐷 has mirror symmetry in line 𝐴 𝐹 . Given that 𝐸 𝐷 = 1 0 and 𝐵 𝐶 = 1 0 . 8 , calculate the perimeters of 𝐴 𝐶 𝐹 𝐷 and 𝐵 𝐶 𝐷 .

  • Aperimeter of 𝐴 𝐶 𝐹 𝐷 = 4 7 . 9 , perimeter of 𝐵 𝐶 𝐷 = 3 1 . 6
  • Bperimeter of 𝐴 𝐶 𝐹 𝐷 = 2 7 . 1 , perimeter of 𝐵 𝐶 𝐷 = 2 0 . 8
  • Cperimeter of 𝐴 𝐶 𝐹 𝐷 = 5 4 . 2 , perimeter of 𝐵 𝐶 𝐷 = 5 2
  • Dperimeter of 𝐴 𝐶 𝐹 𝐷 = 5 4 . 2 , perimeter of 𝐵 𝐶 𝐷 = 4 1 . 6

Q12:

Segment 𝐶 𝐷 has mirror symmetry in line 𝐴 𝐹 . Given that 𝐸 𝐷 = 4 and 𝐵 𝐶 = 4 . 3 , calculate the perimeters of 𝐴 𝐶 𝐹 𝐷 and 𝐵 𝐶 𝐷 .

  • Aperimeter of 𝐴 𝐶 𝐹 𝐷 = 2 0 . 7 , perimeter of 𝐵 𝐶 𝐷 = 1 2 . 6
  • Bperimeter of 𝐴 𝐶 𝐹 𝐷 = 1 2 . 4 , perimeter of 𝐵 𝐶 𝐷 = 8 . 3
  • Cperimeter of 𝐴 𝐶 𝐹 𝐷 = 2 4 . 8 , perimeter of 𝐵 𝐶 𝐷 = 2 1 . 4
  • Dperimeter of 𝐴 𝐶 𝐹 𝐷 = 2 4 . 8 , perimeter of 𝐵 𝐶 𝐷 = 1 6 . 6

Q13:

In the figure, 𝐷 𝐵 𝐶 is symmetrical about line 𝐿 . If 𝑚 𝐶 = 6 1 , what is 𝑚 𝐴 𝐵 𝐷 ?

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