# Worksheet: Conditions for Triangle Congruence

In this worksheet, we will practice identifying congruent triangles by applying SSS, SAS, and ASA criteria.

Q1:

The shape in the given figure is a parallelogram.

What can be said of the lengths of and ?

• AThey are equal.
• BThey are different.

Which angle has the same measure as ?

• A
• B
• C
• D
• E

Which angle has the same measure as ?

• A
• B
• C
• D
• E

Given the information gained from the previous sections and the congruence criterion, are triangles and congruent?

• ANo
• BYes

Q2:

State whether the figures are congruent or not congruent.

• Anot congruent
• Bcongruent

Q3:

Each of 32 students in a class have three straws with lengths of 3 inches, 4 inches, and 6 inches, with which they make a triangle. What would be true of all the triangles that they make?

• A They would all be isosceles.
• B They would all be equilateral.
• C They would all be acute triangles.
• D They would all be congruent.
• E They would all be right triangles.

Q4:

The diagonal of the rectangle divides its surface into two triangles.

• A congruent
• B different

Q5:

In the figure, .

Which congruence criterion could be used to prove the two triangles are congruent?

• A The SAS rule will prove congruence.
• B The AAS rule will prove congruence.
• C The ASA rule will prove congruence.
• DThere is not enough information to prove congruence.
• E The AAA rule will prove congruence.

Q6:

In the given figure, is the perpendicular bisector of . By definition, is equal to , is a common side to both angles, and and are both right angles.

Which congruence criterion could be used to prove that triangle and triangle are congruent?

• A ASA
• B SSS
• C SAS

As triangle and triangle are congruent, determine what will be true of the line segments and , wherever may lie on the line.

• AThey will be congruent.
• BThey will be parallel.
• CThey will be perpendicular.

Q7:

Complete the sentence: These figures are .

• Asimilar but not congruent
• Bneither similar nor congruent
• Ccongruent

Q8:

The two triangles in the given figure have equal sides. Are the two triangles congruent?

• A yes
• B no