# Worksheet: Congruence of Triangles: ASA and AAS

In this worksheet, we will practice proving that two triangles are congruent using either the angle-side-angle (ASA) or the angle-angle-side (AAS) criterion and determining whether angle-side-side is a valid criterion for triangle congruence or not.

Q1:

Determine the lengths of and .

• A ,
• B ,
• C ,
• D ,

Q2:

Which congruence criteria can be used to prove that the two triangles in the given figure are congruent?

• AASA
• BSSS
• CSAS

Q3:

Which congruence criteria can be used to prove that the two triangles in the given figure are congruent?

• ASSS
• BASA
• CSAS

Q4:

Find the lengths of and .

• A ,
• B ,
• C ,
• D ,

Q5:

The two triangles in the given figure share the measures of two angles and the length of one side. Does a rigid transformation exist that would map triangle to triangle , and, hence, are the two triangles congruent?

• Ayes
• Bno

Q6:

Two triangles have two corresponding angles and one corresponding side that are equal. Are the two triangles congruent?

• Ano
• Byes

Q7:

Determine whether the triangles in the given figure are congruent, and, if they are, state which of the congruence criteria proves this.

• Acongruent, ASA
• Bnot congruent
• Ccongruent, SAS
• Dcongruent, SSS

Q8:

Two triangles contain angles of equal measures.

Can we prove that the triangles are similar?

• Ano
• Byes

Can we prove that the two triangles are congruent?

• Ano
• Byes

Q9:

In the given figure, a reflection in the line would map triangle to triangle . Does it follow that the two triangles congruent?

• Ayes
• Bno

Q10:

Find the length of .

Q11:

Are two triangles congruent only when the angles of one triangle are equal to the angles in the other?

• AYes
• BNo

Q12:

Triangle has been rotated to obtain triangle as seen in the given figure.

What is the measure of ?

What is the length of ?

What is the measure of ?

What type of triangle is ?

• Ascalene
• Bequilateral
• Cisosceles

Q13:

Which is the correct congruence from this figure?

• A
• B
• C
• D

Q14:

In the given figure, and . Find .

Q15:

The triangle in the given figure has been constructed in the following way: is the midpoint of , is the line parallel to , and is the line parallel to .

What do we know about the measures of angles and ?

• AAngle is bigger than angle .
• BAngle is bigger than angle .
• CThey are equal.

What do we know about the measures of angles and ?

• AAngle is bigger than angle .
• BThey are equal.
• CAngle is bigger than angle .

What do we know about the lengths of and ?

• A is longer than .
• B is longer than .
• CThey are equal.

Are triangles and congruent? If yes, state by which congruence criteria.

• AYes, AAA
• BYes, SAS
• CYes, ASA
• DNo
• EYes, SSS

Therefore, what can be said of the lengths , , , and ?

• A and
• B and
• C and
• D and
• E and

Since is a parallelogram, what can be said of the points and ?

• AWe cannot conclude anything.
• B and are midpoints, because and .
• C is closer to than because is less than .
• D is closer to than because is less than .

Q16:

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?

• ASSS
• BASA
• CSAS

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.

Q17:

In the figure, .

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

• AThe SAS rule will prove congruence.
• BThe AAS rule will prove congruence.
• CThe AAA rule will prove congruence.
• DThe ASA rule will prove congruence.
• EThere is not enough information to prove congruence.

Q18:

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 ASA congruence criterion, are triangles and congruent?

• AYes
• BNo