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Worksheet: Application of Congruence of Polygons

Q1:

Find 𝑆 π‘Š in the given figure.

Q2:

Find 𝑆 π‘Š in the given figure.

Q3:

If β–³ 𝐿 𝑀 𝑁 β‰… β–³ 𝑄 𝑅 𝑆 , find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 4 . 4 , 𝑦 = 1 1
  • B π‘₯ = 5 , 𝑦 = 3 . 7
  • C π‘₯ = 4 . 4 , 𝑦 = 3 . 7
  • D π‘₯ = 5 , 𝑦 = 1 1
  • E π‘₯ = 3 5 , 𝑦 = 5 . 5

Q4:

If β–³ 𝐿 𝑀 𝑁 β‰… β–³ 𝑄 𝑅 𝑆 , find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 1 5 . 5 , 𝑦 = 8
  • B π‘₯ = 3 1 , 𝑦 = 5 . 3
  • C π‘₯ = 1 5 . 5 , 𝑦 = 5 . 3
  • D π‘₯ = 3 1 , 𝑦 = 8
  • E π‘₯ = 3 1 , 𝑦 = 1 6

Q5:

Given that β–³ 𝑃 𝑄 𝑆 β‰… β–³ 𝑅 𝑄 𝑆 , find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 5 9 1 9 , 𝑦 = 1 9 1 7
  • B π‘₯ = 3 1 1 7 , 𝑦 = 6 2 1 7
  • C π‘₯ = 4 , 𝑦 = 1 2
  • D π‘₯ = 8 , 𝑦 = 4
  • E π‘₯ = 1 7 1 0 4 , 𝑦 = 1 7 2 0 8

Q6:

Given that β–³ 𝑃 𝑄 𝑆 β‰… β–³ 𝑅 𝑄 𝑆 , find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 6 2 2 5 , 𝑦 = 1 9 4 6
  • B π‘₯ = 1 1 5 2 3 , 𝑦 = 6 1 4 2 3
  • C π‘₯ = 6 , 𝑦 = 1 0
  • D π‘₯ = 8 , 𝑦 = 2
  • E π‘₯ = 2 3 1 5 2 , 𝑦 = 2 3 6 0 8

Q7:

The perimeter of the polygon 𝐴 𝐡 𝐢 𝐷 𝐸 is 176 cm and 𝐴 𝐡 𝐢 𝐷 𝐸 β‰… 𝐹 𝑀 𝐿 𝐷 𝐸 . Given that 𝐸 ∈ βƒ–     βƒ— 𝐴 𝐹 and 𝐷 𝐸 = 4 8 c m , find the perimeter of the figure 𝐴 𝐡 𝐢 𝐷 𝐿 𝑀 𝐹 .

Q8:

𝐴 𝐡 𝐢 𝐷 β‰… 𝑀 𝐹 𝐸 𝐷 and 𝐢 is the midpoint of 𝑀 𝐷 . Given that 𝑀 𝐢 = 3 8 . 1 c m , find the length of 𝐴 𝐸 .

Q9:

Given that the polygons 𝐴 𝐡 𝐢 𝐷 and 𝐸 𝐹 𝐺 𝐻 are congruent, find the perimeter of the polygon 𝐴 𝐡 𝐢 𝐷 and then π‘š ∠ 𝐹 .

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

Q10:

If ∠ 𝐴 is congruent to ∠ 𝐡 and π‘š ∠ 𝐴 = 8 1 ∘ , what is π‘š ∠ 𝐡 ?

Q11:

In the figure, is congruent to . Given that and , find .

  • A
  • B
  • C
  • D

Q12:

Consider two congruent triangles: β–³ 𝐷 𝐸 𝐹 and β–³ 𝑂 𝑃 𝑄 . Which angle in β–³ 𝑂 𝑃 𝑄 corresponds to ∠ 𝐸 ?

  • A ∠ 𝑄
  • B ∠ 𝑂
  • C ∠ 𝑃

Q13:

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

Q14:

If the polygon 𝐴 𝐡 𝐢 𝐷 𝑀 𝐿 β‰… the polygon 𝐾 𝑍 π‘Œ 𝑋 𝑀 𝐿 , 𝐴 𝐡 = 8 . 3 cm, and 𝐡 𝐢 = 6 cm, find the perimeter of the polygon 𝑀 𝑋 π‘Œ 𝑍 𝐾 𝐿 .

Q15:

Given that β–³ 𝐴 𝐡 𝐢 β‰… β–³ 𝑋 π‘Œ 𝑍 , find the length of 𝑋 π‘Œ and calculate the perimeter of β–³ 𝑋 π‘Œ 𝑍 .

  • A 𝑋 π‘Œ = 2 5 c m , the perimeter = 5 7 c m
  • B 𝑋 π‘Œ = 7 c m , the perimeter = 3 9 c m
  • C 𝑋 π‘Œ = 2 2 c m , the perimeter = 5 4 c m

Q16:

Find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 4 . 5 , 𝑦 = 5 8
  • B π‘₯ = 5 . 1 , 𝑦 = 7 6
  • C π‘₯ = 3 . 8 , 𝑦 = 4 6
  • D π‘₯ = 3 . 8 , 𝑦 = 7 6

Q17:

Find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 6 , 𝑦 = 6 4
  • B π‘₯ = 6 . 3 , 𝑦 = 7 2
  • C π‘₯ = 4 . 6 , 𝑦 = 4 4
  • D π‘₯ = 4 . 6 , 𝑦 = 7 2

Q18:

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

Q19:

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

Q20:

Given that the two polygons shown are congruent, find the length of 𝑁 𝐾 .

Q21:

In the figure pentagon 𝐴 𝐡 𝐢 𝐷 𝐸 is congruent to pentagon 𝐻 𝐼 𝐽 𝐹 𝐺 .

Work out the length of 𝐡 𝐢 .

Work out the length of 𝐼 𝐻 .

Work out the length of 𝐺 𝐻 .

Work out the measure of angle 𝐴 𝐡 𝐢 .

Work out the measure of angle 𝐹 𝐺 𝐻 .

Q22:

Given that is congruent to , , and , find .

  • A
  • B
  • C
  • D
  • E

Q23:

Consider two congruent polygons 𝐴 𝐡 𝐢 𝐷 and 𝑋 π‘Œ 𝑍 𝐿 . First, write the line segment in 𝑋 π‘Œ 𝑍 𝐿 that corresponds to 𝐷 𝐴 . Then, find the angle in 𝑋 π‘Œ 𝑍 𝐿 whose measure is the same as π‘š ∠ 𝐡 𝐢 𝐷 .

  • A π‘Œ 𝑍 , ∠ 𝐿 𝑋 π‘Œ
  • B 𝑋 π‘Œ , ∠ 𝑍 𝐿 𝑋
  • C 𝑍 𝐿 , ∠ 𝑋 π‘Œ 𝑍
  • D 𝐿 𝑋 , ∠ π‘Œ 𝑍 𝐿

Q24:

What is the condition for two angles to be congruent?

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

Q25:

In the given figure, 𝐴 𝐡 and 𝐷 𝐸 are parallel and 𝐢 lies on both 𝐡 𝐷 and 𝐴 𝐸 .

Work out the value of π‘₯ .

Are triangles 𝐴 𝐡 𝐢 and 𝐸 𝐷 𝐢 congruent?

  • Ayes
  • Bno