Worksheet: Applications on Congruent Triangles

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

Q1:

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

  • Ano
  • Byes

Q2:

In the given figure, △𝐴𝐵𝐶≅△𝐿𝑀𝑁. Determine 𝑚∠𝑁.

Q3:

In the following figure, find 𝑚∠𝐽𝐾𝐿.

Q4:

Given that △𝐹𝐺𝐻≅△𝐾𝐿𝑀, 𝑚∠𝐹=83∘, and 𝑚∠𝐻=83∘, determine 𝑚∠𝐿.

Q5:

Determine the value of 𝑥 in the given congruent triangles.

Q6:

In the following figure, find 𝑚∠𝑃𝑄𝑆.

Q7:

Given that △𝑅𝑆𝑉≅△𝑇𝑉𝑆, find the values of 𝑥 and 𝑦.

  • A𝑥=61, 𝑦=46
  • B𝑥=29, 𝑦=38
  • C𝑥=29, 𝑦=46
  • D𝑥=61, 𝑦=23
  • E𝑥=29, 𝑦=23

Q8:

In the figure, 𝐵𝐷 meets 𝐴𝐸 at 𝐶, which is also the midpoint of 𝐵𝐷. Find the length of 𝐶𝐸.

Q9:

Given that △𝐴𝐵𝐶≅△𝑋𝑌𝑍, and 𝑚∠𝐴+𝑚∠𝐵=117∘, what is 𝑚∠𝑍?

Q10:

Given that 𝐴𝐵𝐶𝐷 is a square, find 𝑚∠𝑌𝐶𝐵.

Q11:

From the information in the figure, what is 𝑚∠𝐵𝑀𝐶?

Q12:

In the figure below, 𝐷𝑋𝑌𝐸 is a rectangle. Find 𝑚∠𝐴𝐸𝐷.

Q13:

Triangles 𝐴𝐵𝐶 and 𝐸𝐷𝐹 are congruent. What is the perimeter of △𝐴𝐵𝐶?

Q14:

Consider the figure, then complete the following using <, =, or >: 𝑋𝑌𝑋𝑊.

  • A<
  • B=
  • C>

Q15:

Given that 𝐵𝐶=𝐴𝐷, 𝐴𝐶=𝐴𝐸, and 𝑚∠𝐶𝐴𝐵=68∘, find 𝑚∠𝐸𝐴𝐷.

Q16:

Given that △𝐴𝐸𝐶 and △𝐵𝐹𝐷 are congruent, what is the measure of ∠𝐵𝐷𝐹?

Q17:

Given that triangle 𝐴𝐵𝐶 is congruent to triangle 𝑋𝑌𝑍, find 𝑚∠𝐵.

  • A52∘
  • B74∘
  • C42∘
  • D54∘

Q18:

Find 𝑚∠𝐵𝐴𝐸.

Q19:

The two triangles in the given figure are congruent. Work out the area of triangle 𝐴𝐵𝐶.

Q20:

If △𝐴𝐵𝐶≅△𝐴𝐵𝐷, the perimeter of 𝐴𝐶𝐵𝐷=394cm, and 𝐴𝐵=56cm, find the perimeter of △𝐴𝐵𝐶.

Q21:

Given that △𝐴𝐵𝐶≅△𝐴𝐵𝐷, find the perimeter of 𝐴𝐶𝐵𝐷.

Q22:

Given that △𝐴𝐵𝐶 is congruent to △𝑋𝑌𝑍, first find the length in △𝑋𝑌𝑍 that is equal to 𝐴𝐵. Then find the angle in △𝐴𝐵𝐶 with the same measure as ∠𝑍.

  • A𝑌𝑍, ∠𝐵
  • B𝑋𝑌, ∠𝐶
  • C𝑋𝑍, ∠𝐴

Q23:

In the figure, △𝐴𝐵𝐶 and △𝐸𝐹𝐷 are congruent.

Work out the length of 𝐵𝐶.

Work out the length of 𝐸𝐹.

Work out the measure of angle 𝐷𝐸𝐹.

Q24:

In the figure shown, 𝑚∠𝐵𝐷𝐸=50∘. What is 𝑚∠𝐸𝐴𝐶?

Q25:

Suppose △𝐴𝐵𝐶≅△𝑋𝑌𝑍. If the perimeter of △𝐴𝐵𝐶 is 14, 𝑋𝑌=3, and 𝑌𝑍=5, what is 𝐴𝐶?

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