Worksheet: Congruence of Triangles

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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, △ 𝐴 𝐵 𝐶 ≅ △ 𝐿 𝑀 𝑁 . Determine 𝑚 ∠ 𝑁 .

Q3:

In the following figure, find 𝑚 ∠ 𝐽 𝐾 𝐿 .

Q4:

Given that △ 𝐹 𝐺 𝐻 ≅ △ 𝐾 𝐿 𝑀 , 𝑚 ∠ 𝐹 = 8 3 ∘ , and 𝑚 ∠ 𝐻 = 8 3 ∘ , determine 𝑚 ∠ 𝐿 .

Q5:

Determine the value of 𝑥 in the given congruent triangles.

Q6:

In the following figure, find 𝑚 ∠ 𝑃 𝑄 𝑆 .

Q7:

Given that △ 𝑅 𝑆 𝑉 ≅ △ 𝑇 𝑉 𝑆 , find the values of 𝑥 and 𝑦 .

  • A 𝑥 = 2 9 , 𝑦 = 2 3
  • B 𝑥 = 2 9 , 𝑦 = 4 6
  • C 𝑥 = 2 9 , 𝑦 = 3 8
  • D 𝑥 = 6 1 , 𝑦 = 2 3
  • E 𝑥 = 6 1 , 𝑦 = 4 6

Q8:

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

Q9:

Given that △ 𝐴 𝐵 𝐶 ≅ △ 𝑋 𝑌 𝑍 , and 𝑚 ∠ 𝐴 + 𝑚 ∠ 𝐵 = 1 1 7 ∘ , what is 𝑚 ∠ 𝑍 ?

Q10:

Given that 𝐴 𝐵 𝐶 𝐷 is a square, find 𝑚 ∠ 𝑌 𝐶 𝐵 .

Q11:

From the information in the figure, what is 𝑚 ∠ 𝐵 𝑀 𝐶 ?

Q12:

In the figure below, 𝐷 𝑋 𝑌 𝐸 is a rectangle. Find 𝑚 ∠ 𝐴 𝐸 𝐷 .

Q13:

Triangles 𝐴 𝐵 𝐶 and 𝐸 𝐷 𝐹 are congruent. What is the perimeter of △ 𝐴 𝐵 𝐶 ?

Q14:

Consider the figure, then complete the following using < , = , or > : 𝑋 𝑌 𝑋 𝑊 .

  • A =
  • B <
  • C >

Q15:

Given that 𝐵 𝐶 = 𝐴 𝐷 , 𝐴 𝐶 = 𝐴 𝐸 , and 𝑚 ∠ 𝐶 𝐴 𝐵 = 6 8 ∘ , find 𝑚 ∠ 𝐸 𝐴 𝐷 .

Q16:

Given that △ 𝐴 𝐸 𝐶 and △ 𝐵 𝐹 𝐷 are congruent, what is the measure of ∠ 𝐵 𝐷 𝐹 ?

Q17:

Given that triangle 𝐴 𝐵 𝐶 is congruent to triangle 𝑋 𝑌 𝑍 , find 𝑚 ∠ 𝐵 .

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

Q18:

Find 𝑚 ∠ 𝐵 𝐴 𝐸 .

Q19:

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

Q20:

If △ 𝐴 𝐵 𝐶 ≅ △ 𝐴 𝐵 𝐷 , the perimeter of 𝐴 𝐶 𝐵 𝐷 = 3 9 4 c m , and 𝐴 𝐵 = 5 6 c m , find the perimeter of △ 𝐴 𝐵 𝐶 .

Q21:

Given that △ 𝐴 𝐵 𝐶 ≅ △ 𝐴 𝐵 𝐷 , find the perimeter of 𝐴 𝐶 𝐵 𝐷 .

Q22:

Given that △ 𝐴 𝐵 𝐶 is congruent to △ 𝑋 𝑌 𝑍 , first find the length in △ 𝑋 𝑌 𝑍 that is equal to 𝐴 𝐵 . Then find the angle in △ 𝐴 𝐵 𝐶 with the same measure as ∠ 𝑍 .

  • A 𝑌 𝑍 , ∠ 𝐵
  • B 𝑋 𝑍 , ∠ 𝐴
  • C 𝑋 𝑌 , ∠ 𝐶

Q23:

In the figure, △ 𝐴 𝐵 𝐶 and △ 𝐸 𝐹 𝐷 are congruent.

Work out the length of 𝐵 𝐶 .

Work out the length of 𝐸 𝐹 .

Work out the measure of angle 𝐷 𝐸 𝐹 .

Q24:

In the figure shown, 𝑚 ∠ 𝐵 𝐷 𝐸 = 5 0 ∘ . What is 𝑚 ∠ 𝐸 𝐴 𝐶 ?

Q25:

Suppose △ 𝐴 𝐵 𝐶 ≅ △ 𝑋 𝑌 𝑍 . If the perimeter of △ 𝐴 𝐵 𝐶 is 14, 𝑋 𝑌 = 3 , and 𝑌 𝑍 = 5 , what is 𝐴 𝐶 ?

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