# Lesson Worksheet: Applications on Congruent Triangles Mathematics • 8th Grade

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 ?