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Worksheet: Congruence of Triangles

In this worksheet, we will practice identifying congruence in triangles using different criteria and using this to find unknown angles or sides.

Q1:

Are two triangles congruent if both triangles have the same side lengths?

  • Ayes
  • Bno

Q2:

In the given figure, . Determine .

  • A
  • B
  • C
  • D
  • E

Q3:

In the following figure, find .

  • A
  • B
  • C
  • D
  • E

Q4:

Given that , , and , determine .

  • A
  • B
  • C
  • D
  • E

Q5:

Determine the value of π‘₯ in the given congruent triangles.

Q6:

In the following figure, find π‘š ∠ 𝑃 𝑄 𝑆 .

  • A 8 6 ∘
  • B 4 7 ∘
  • C 9 4 ∘
  • D 4 3 ∘
  • E 9 0 ∘

Q7:

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

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

Q8:

In the figure, 𝐡 𝐷 meets 𝐴 𝐸 at 𝐢 , which is also the midpoint of 𝐡 𝐷 . Find the length of 𝐢 𝐸 .

Q9:

Given that β–³ 𝐴 𝐡 𝐢 β‰… β–³ 𝑋 π‘Œ 𝑍 , and π‘š ∠ 𝐴 + π‘š ∠ 𝐡 = 1 1 7 ∘ , what is π‘š ∠ 𝑍 ?

Q10:

Given that 𝐴 𝐡 𝐢 𝐷 is a square, find π‘š ∠ π‘Œ 𝐢 𝐡 .

Q11:

From the information in the figure, what is π‘š ∠ 𝐡 𝑀 𝐢 ?

Q12:

In the figure below, 𝐷 𝑋 π‘Œ 𝐸 is a rectangle. Find π‘š ∠ 𝐴 𝐸 𝐷 .

Q13:

Triangles 𝐴 𝐡 𝐢 and 𝐸 𝐷 𝐹 are congruent. What is the perimeter of β–³ 𝐴 𝐡 𝐢 ?

Q14:

Consider the figure, then complete the following using < , = , or > : 𝑋 π‘Œ 𝑋 π‘Š .

  • A <
  • B >
  • C =

Q15:

Given that 𝐡 𝐢 = 𝐴 𝐷 , 𝐴 𝐢 = 𝐴 𝐸 , and π‘š ∠ 𝐢 𝐴 𝐡 = 6 8 ∘ , find π‘š ∠ 𝐸 𝐴 𝐷 .

Q16:

Given that β–³ 𝐴 𝐸 𝐢 and β–³ 𝐡 𝐹 𝐷 are congruent, what is the measure of ∠ 𝐡 𝐷 𝐹 ?

Q17:

Given that triangle 𝐴 𝐡 𝐢 is congruent to triangle 𝑋 π‘Œ 𝑍 , find π‘š ∠ 𝐡 .

  • A 7 4 ∘
  • B 5 4 ∘
  • C 4 2 ∘
  • D 5 2 ∘

Q18:

Find π‘š ∠ 𝐡 𝐴 𝐸 .

Q19:

The two triangles in the given figure are congruent. Work out the area of triangle 𝐴 𝐡 𝐢 .

Q20:

If β–³ 𝐴 𝐡 𝐢 β‰… β–³ 𝐴 𝐡 𝐷 , the perimeter of 𝐴 𝐢 𝐡 𝐷 = 3 9 4 c m , and 𝐴 𝐡 = 5 6 c m , find the perimeter of β–³ 𝐴 𝐡 𝐢 .

Q21:

Given that β–³ 𝐴 𝐡 𝐢 β‰… β–³ 𝐴 𝐡 𝐷 , find the perimeter of 𝐴 𝐢 𝐡 𝐷 .

Q22:

Given that β–³ 𝐴 𝐡 𝐢 is congruent to β–³ 𝑋 π‘Œ 𝑍 , first find the length in β–³ 𝑋 π‘Œ 𝑍 that is equal to 𝐴 𝐡 . Then find the angle in β–³ 𝐴 𝐡 𝐢 with the same measure as ∠ 𝑍 .

  • A π‘Œ 𝑍 , ∠ 𝐡
  • B 𝑋 𝑍 , ∠ 𝐴
  • C 𝑋 π‘Œ , ∠ 𝐢

Q23:

In the figure, and are congruent.

Work out the length of .

  • A5
  • B2.2
  • C5.4
  • D4.5
  • E4.9

Work out the length of .

  • A2.2
  • B5.4
  • C5
  • D4.5
  • E4.9

Work out the size of angle .

  • A
  • B
  • C
  • D
  • E

Q24:

In the figure shown, π‘š ∠ 𝐡 𝐷 𝐸 = 5 0 ∘ . What is π‘š ∠ 𝐸 𝐴 𝐢 ?

Q25:

Suppose β–³ 𝐴 𝐡 𝐢 β‰… β–³ 𝑋 π‘Œ 𝑍 . If the perimeter of β–³ 𝐴 𝐡 𝐢 is 14, 𝑋 π‘Œ = 3 , and π‘Œ 𝑍 = 5 , what is 𝐴 𝐢 ?

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