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Worksheet: Application of Lines of Symmetry

Q1:

Given that 𝐿 is a line of symmetry for the shape 𝐴 𝐡 𝐢 𝐷 𝐸 , calculate π‘š ∠ 𝐡 𝐢 𝐷 .

Q2:

Given that 𝐿 is a line of symmetry for the shape 𝐴 𝐡 𝐢 𝐷 𝐸 , calculate π‘š ∠ 𝐡 𝐢 𝐷 .

Q3:

In the figure, 𝐴 , 𝐹 , and 𝐡 are collinear, with 𝐴 𝐡 = 1 0 . If βƒ–     βƒ— 𝐹 𝐷 is a line of symmetry of polygon 𝐴 𝐡 𝐢 𝐷 𝐸 , find π‘š ∠ 𝐢 𝐷 𝐸 and the length 𝐡 𝐹 .

  • A π‘š ∠ 𝐢 𝐷 𝐸 = 6 8 ∘ , 𝐡 𝐹 = 1 0
  • B π‘š ∠ 𝐢 𝐷 𝐸 = 6 8 ∘ , 𝐡 𝐹 = 5
  • C π‘š ∠ 𝐢 𝐷 𝐸 = 1 3 6 ∘ , 𝐡 𝐹 = 1 0
  • D π‘š ∠ 𝐢 𝐷 𝐸 = 1 3 6 ∘ , 𝐡 𝐹 = 5

Q4:

In the figure, 𝐴 , 𝐹 , and 𝐡 are collinear, with 𝐴 𝐡 = 1 4 . If βƒ–     βƒ— 𝐹 𝐷 is a line of symmetry of polygon 𝐴 𝐡 𝐢 𝐷 𝐸 , find π‘š ∠ 𝐢 𝐷 𝐸 and the length 𝐡 𝐹 .

  • A π‘š ∠ 𝐢 𝐷 𝐸 = 6 9 ∘ , 𝐡 𝐹 = 1 4
  • B π‘š ∠ 𝐢 𝐷 𝐸 = 6 9 ∘ , 𝐡 𝐹 = 7
  • C π‘š ∠ 𝐢 𝐷 𝐸 = 1 3 8 ∘ , 𝐡 𝐹 = 1 4
  • D π‘š ∠ 𝐢 𝐷 𝐸 = 1 3 8 ∘ , 𝐡 𝐹 = 7

Q5:

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

Q6:

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

Q7:

Given that βƒ–      βƒ— 𝑋 π‘Œ is the line of symmetry of the polygon 𝐴 𝐡 π‘Œ 𝐢 𝐷 , determine the perimeter of 𝐴 𝐡 π‘Œ 𝐢 𝐷 .

Q8:

Given that βƒ–      βƒ— 𝑋 π‘Œ is the line of symmetry of the polygon 𝐴 𝐡 π‘Œ 𝐢 𝐷 , determine the perimeter of 𝐴 𝐡 π‘Œ 𝐢 𝐷 .

Q9:

Segment 𝐢 𝐷 has mirror symmetry in line βƒ–     βƒ— 𝐴 𝐹 . Given that 𝐸 𝐷 = 5 and 𝐡 𝐢 = 5 . 1 , calculate the perimeters of 𝐴 𝐢 𝐹 𝐷 and β–³ 𝐡 𝐢 𝐷 .

  • Aperimeter of 𝐴 𝐢 𝐹 𝐷 = 2 5 , perimeter of β–³ 𝐡 𝐢 𝐷 = 1 5 . 2
  • Bperimeter of 𝐴 𝐢 𝐹 𝐷 = 1 4 . 9 , perimeter of β–³ 𝐡 𝐢 𝐷 = 1 0 . 1
  • Cperimeter of 𝐴 𝐢 𝐹 𝐷 = 2 9 . 8 , perimeter of β–³ 𝐡 𝐢 𝐷 = 2 6 . 6
  • Dperimeter of 𝐴 𝐢 𝐹 𝐷 = 2 9 . 8 , perimeter of β–³ 𝐡 𝐢 𝐷 = 2 0 . 2

Q10:

Segment 𝐢 𝐷 has mirror symmetry in line βƒ–     βƒ— 𝐴 𝐹 . Given that 𝐸 𝐷 = 1 0 and 𝐡 𝐢 = 1 0 . 8 , calculate the perimeters of 𝐴 𝐢 𝐹 𝐷 and β–³ 𝐡 𝐢 𝐷 .

  • Aperimeter of 𝐴 𝐢 𝐹 𝐷 = 4 7 . 9 , perimeter of β–³ 𝐡 𝐢 𝐷 = 3 1 . 6
  • Bperimeter of 𝐴 𝐢 𝐹 𝐷 = 2 7 . 1 , perimeter of β–³ 𝐡 𝐢 𝐷 = 2 0 . 8
  • Cperimeter of 𝐴 𝐢 𝐹 𝐷 = 5 4 . 2 , perimeter of β–³ 𝐡 𝐢 𝐷 = 5 2
  • Dperimeter of 𝐴 𝐢 𝐹 𝐷 = 5 4 . 2 , perimeter of β–³ 𝐡 𝐢 𝐷 = 4 1 . 6

Q11:

Segment 𝐢 𝐷 has mirror symmetry in line βƒ–     βƒ— 𝐴 𝐹 . Given that 𝐸 𝐷 = 4 and 𝐡 𝐢 = 4 . 3 , calculate the perimeters of 𝐴 𝐢 𝐹 𝐷 and β–³ 𝐡 𝐢 𝐷 .

  • Aperimeter of 𝐴 𝐢 𝐹 𝐷 = 2 0 . 7 , perimeter of β–³ 𝐡 𝐢 𝐷 = 1 2 . 6
  • Bperimeter of 𝐴 𝐢 𝐹 𝐷 = 1 2 . 4 , perimeter of β–³ 𝐡 𝐢 𝐷 = 8 . 3
  • Cperimeter of 𝐴 𝐢 𝐹 𝐷 = 2 4 . 8 , perimeter of β–³ 𝐡 𝐢 𝐷 = 2 1 . 4
  • Dperimeter of 𝐴 𝐢 𝐹 𝐷 = 2 4 . 8 , perimeter of β–³ 𝐡 𝐢 𝐷 = 1 6 . 6

Q12:

In the figure, is symmetrical about line . If , what is ?

  • A
  • B
  • C
  • D

Q13:

In the figure, is symmetrical about line . If , what is ?

  • A
  • B
  • C
  • D