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Lesson: Identifying Congruence in Triangles and Finding the Missing Angles or Sides

Worksheet • 25 Questions

Q1:

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

Q2:

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

  • A >
  • B =
  • C <

Q3:

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

Q4:

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

Q5:

Given that , , and , find .

  • A
  • B
  • C
  • D

Q6:

Given that and are congruent, what is the size of ?

  • A
  • B
  • C
  • D

Q7:

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

  • Ano
  • Byes

Q8:

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 ?

Q9:

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

Q10:

Given that is a square, find .

  • A
  • B
  • C
  • D
  • E

Q11:

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

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

Q12:

Find .

  • A
  • B
  • C

Q13:

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

Q14:

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 .

Q15:

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

Q16:

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

Q17:

In the figure below, is a rectangle. Find .

  • A
  • B
  • C
  • D

Q18:

In the figure, β–³ 𝐴 𝐡 𝐢 and β–³ 𝐸 𝐹 𝐷 are congruent.

Work out the length of 𝐡 𝐢 .

Work out the length of 𝐸 𝐹 .

Work out the measure of angle 𝐷 𝐸 𝐹 .

Q19:

In the figure shown, . What is ?

  • A
  • B
  • C
  • D

Q20:

Given that β–³ 𝐹 𝐺 𝐻 β‰… β–³ 𝐾 𝐿 𝑀 , π‘š ∠ 𝐹 = 8 3 ∘ , and π‘š ∠ 𝐻 = 8 3 ∘ , determine π‘š ∠ 𝐿 .

Q21:

Given that β–³ 𝐹 𝐺 𝐻 β‰… β–³ 𝐾 𝐿 𝑀 , π‘š ∠ 𝐹 = 6 8 ∘ , and π‘š ∠ 𝐻 = 6 8 ∘ , determine π‘š ∠ 𝐿 .

Q22:

From the information in the figure, what is ?

  • A
  • B
  • C
  • D

Q23:

In the given figure, β–³ 𝐴 𝐡 𝐢 β‰… β–³ 𝐿 𝑀 𝑁 . Determine π‘š ∠ 𝑁 .

Q24:

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

Q25:

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

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