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.
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:
In the figure, .
- 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