Worksheet: Applications on Congruent Triangles

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, 𝐴𝐵𝐶𝐿𝑀𝑁. Determine 𝑚𝑁.

Q3:

In the following figure, find 𝑚𝐽𝐾𝐿.

Q4:

Given that 𝐹𝐺𝐻𝐾𝐿𝑀, 𝑚𝐹=83, and 𝑚𝐻=83, determine 𝑚𝐿.

Q5:

Determine the value of 𝑥 in the given congruent triangles.

Q6:

In the following figure, find 𝑚𝑃𝑄𝑆.

Q7:

Given that 𝑅𝑆𝑉𝑇𝑉𝑆, 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 𝐴𝐵𝐶𝑋𝑌𝑍, and 𝑚𝐴+𝑚𝐵=117, what is 𝑚𝑍?

Q10:

Given that 𝐴𝐵𝐶𝐷 is a square, find 𝑚𝑌𝐶𝐵.

Q11:

From the information in the figure, what is 𝑚𝐵𝑀𝐶?

Q12:

In the figure below, 𝐷𝑋𝑌𝐸 is a rectangle. Find 𝑚𝐴𝐸𝐷.

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 𝑚𝐶𝐴𝐵=68, find 𝑚𝐸𝐴𝐷.

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 𝑚𝐵.

  • A52
  • B74
  • C42
  • D54

Q18:

Find 𝑚𝐵𝐴𝐸.

Q19:

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

Q20:

If 𝐴𝐵𝐶𝐴𝐵𝐷, the perimeter of 𝐴𝐶𝐵𝐷=394cm, and 𝐴𝐵=56cm, find the perimeter of 𝐴𝐵𝐶.

Q21:

Given that 𝐴𝐵𝐶𝐴𝐵𝐷, 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, 𝑚𝐵𝐷𝐸=50. What is 𝑚𝐸𝐴𝐶?

Q25:

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

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