Start Practicing
Worksheet: Proving Triangle Congruence Using ASA and AAS Criteria
Q1:
Two triangles have two corresponding angles and one corresponding side that are equal. Are the two triangles congruent?
- A yes
- B no
Q2:
Determine whether the triangles in the given figure are congruent, and, if they are, state which of the congruence criteria proves this.
- A congruent,
- B congruent,
- C not congruent
- D congruent,
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:
Which congruence criteria can be used to prove that the two triangles in the given figure are congruent?
- A SAS
- B SSS
- C ASA
Q5:
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
Q6:
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
Q7:
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:
Find the lengths of and .
- A ,
- B ,
- C ,
- D ,
Q12:
Are two triangles congruent when the angles of one triangle are equal to the angles in the other?
- A no
- B yes
Q13:
In the following figure, find .
Q14:
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 ?
- Aisosceles
- Bscalene
- Cequilateral
Q15:
Which is the correct congruence from this figure?
- A
- B
- C
- D
Q16:
In the given figure, and . Find .
Q17:
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 ?
- 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 .