# 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, . Determine . Q3:

In the following figure, find . Q4:

Given that , , and , determine . Q5:

Determine the value of in the given congruent triangles. Q6:

In the following figure, find . Q7:

Given that , find the values of and . • A,
• B,
• C,
• D,
• E,

Q8:

In the figure, meets at , which is also the midpoint of . Find the length of . Q9:

Given that , and , what is ?

Q10:

Given that is a square, find . Q11:

From the information in the figure, what is ? Q12:

In the figure below, is a rectangle. Find . Q13:

Triangles and are congruent. What is the perimeter of ? Q14:

Consider the figure, then complete the following using , , or : . • A
• B
• C

Q15:

Given that , , and , find . Q16:

Given that and are congruent, what is the measure of ? Q17:

Given that triangle is congruent to triangle , find . • A
• B
• C
• D

Q18:

Find . Q19:

The two triangles in the given figure are congruent. Work out the area of triangle . Q20:

If , the perimeter of , and , find the perimeter of . Q21:

Given that , find the perimeter of . Q22:

Given that is congruent to , first find the length in that is equal to . Then find the angle in with the same measure as .

• A,
• B,
• C,

Q23:

In the figure, and are congruent. Work out the length of .

Work out the length of .

Work out the measure of angle .

Q24:

In the figure shown, . What is ? Q25:

Suppose . If the perimeter of is 14, , and , what is ?