Worksheet: Application of Congruence of Polygons

In this worksheet, we will practice using congruence of polygons to find a missing angle measure or side length.

Q1:

Find in the given figure.

Q2:

If , find the values of and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q3:

Complete the sentence: These figures are .

• Aneither similar nor congruent
• Bsimilar but not congruent
• Ccongruent

Q4:

The two quadrilaterals in the given figure are congruent. Work out the perimeter of .

Q5:

If , find the values of and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q6:

Given that the two polygons shown are congruent, find the length of .

Q7:

In the figure, is congruent to . Given that and , find .

Q8:

Given that the polygons and are congruent, find the perimeter of the polygon and then .

• A 72 cm,
• B 352 cm,
• C 55 cm,
• D 72 cm,

Q9:

In the figure pentagon is congruent to pentagon .

Work out the length of .

• A5
• B2.2
• C5.8
• D3.2
• E81.9

Work out the length of .

• A2.2
• B5.8
• C5
• D3.2
• E59

Work out the length of .

• A81.9
• B3.2
• C5
• D2.2
• E5.8

Work out the size of angle .

• A
• B
• C
• D
• E

Work out the size of angle .

• A
• B
• C
• D
• E

Q10:

In the given figure, and are parallel and lies on both and .

Work out the value of .

Are triangles and congruent?

• Ayes
• Bno

Q11:

Find the values of and .

• A ,
• B ,
• C ,
• D ,

Q12:

In the following figure, find the length of .

Q13:

Given that , find the values of and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q14:

and is the midpoint of . Given that , find the length of .

Q15:

If is congruent to and , what is ?

Q16:

Consider two congruent triangles: and . Which angle in corresponds to ?

• A
• B
• C

Q17:

Given that the dashed line is a line of symmetry of , which angle has the same size as ?

• A
• B
• C
• D

Q18:

Given that is congruent to , , and , find .

Q19:

Consider two congruent polygons and . First, write the line segment in that corresponds to . Then, find the angle in whose measure is the same as .

• A ,
• B ,
• C ,
• D ,

Q20:

What is the condition for two angles to be congruent?

• Bequal in length
• Cdifferent in length
• Dequal in measure

Q21:

The perimeter of the polygon is 176 cm and . Given that and , find the perimeter of the figure .

Q22:

If the polygon the polygon , cm, and cm, find the perimeter of the polygon .

Q23:

Given that , find the length of and calculate the perimeter of .

• A , the perimeter
• B , the perimeter
• C , the perimeter

Q24:

In a test, you are shown two congruent squares. One square has a side length of 6. What is the perimeter of the other?

Q25:

In the following figure, , , and are three congruent and intersecting rectangles. Find .