In this worksheet, we will practice identifying congruence in triangles using ASA and AAS criteria and finding a missing angle or side length.

**Q2: **

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

- A SAS
- B SSS
- C ASA

**Q3: **

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

- A SAS
- B SSS
- C ASA

**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?

- A yes
- B no

**Q6: **

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

- A yes
- B no

**Q7: **

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

- A congruent, SSS
- B congruent, SAS
- C not congruent
- D congruent, ASA

**Q8: **

Two triangles contain angles of equal measures.

Can we prove that the triangles are similar?

- Ayes
- Bno

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?

- A yes
- B no

**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?

- A No
- B Yes

**Q12: **

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

What is the size of ?

- A
- B
- C
- D

What is the length of ?

- A5
- B4
- C3
- D2

What is the size of ?

- A
- B
- C
- D

What type of triangle is ?

- Aisosceles
- Bscalene
- Cequilateral

**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 sizes of angles and ?

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

What do we know about the sizes of angles and ?

- AThey are equal.
- BAngle is bigger than angle .
- 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,
- Byes,
- Cyes,
- Dno
- Eyes,

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 ?

- A is closer to than because is less than .
- B and are midpoints, because and .
- CWe cannot conclude anything.
- D is closer to than because is less than .