# Lesson Worksheet: Congruence of Triangles: ASA and AAS Mathematics • 8th Grade

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.

**Q3: **

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

- ASSS
- BASA
- CSAS

**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

**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

**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

**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: **

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