# Worksheet: Proving Triangles' Congruence Using SSS and SAS Criterions

Q1:

Which of the following statements will be true for two triangles that are congruent?

• AThere will be only translation that could be used to map one triangle onto the other.
• BThere will always exist a combination of translations, reflections, rotations, and dilations that could be used to map one triangle onto the other.
• CThere will be only reflection that could be used to map one triangle onto the other.
• DThere will always exist a combination of translations, reflections, and rotations that could be used to map one triangle onto the other.
• EThere will be only rotation that could be used to map one triangle onto the other.

Q2:

Two triangles share two sides and a contained angle. Would the two triangles be congruent?

• A yes
• B no

Q3:

In the given figure, triangle and triangle have two equal sides and share one equal angle. Are triangles and congruent?

• A no
• B yes

Q4:

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,

Q5:

Determine whether the triangles in the given figure are congruent by applying SSS, SAS, or ASA. If they are congruent, state which of the congruence criteria proves this.

• A yes, ASA
• B yes, SAS
• C no
• D yes, SSS

Q6:

Can you use to prove the triangles in the given figure are congruent? Please state your reason.

• A no, because the angle must be contained between the two sides
• B yes, because there are two pairs of corresponding sides equal in length and one pair of equal angles

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,
• B congruent,
• C not congruent
• D congruent,

Q8:

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

• A ASA
• B SAS
• C SSS

Q9:

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

• A
• B
• C

Q10:

Given that is the midpoint of in the given figure, without referencing angles, which congruence criteria could you use to prove triangles and are congruent?

• A
• B
• C

Q11:

In the given quadrilateral, and have the same length and and have the same length.

Which angle has the same measure as ?

• A
• B
• C
• D
• E

Hence, are the triangles and congruent? If yes, state which congruence criteria proves this.

• Ano
• Byes, ASA
• Cyes, SSS
• Dyes, SAS

Q12:

The given figure shows an isosceles triangle, where is the midpoint of .

Can we prove that triangle and triangle are congruent? If yes, state which congruence criteria could be used.

• Ayes,
• Bno
• Cyes,
• Dyes,

Hence, what can we conclude about the angles and ?

• AThe angles have the same measure, because the triangles are congruent
• BThe angle is bigger than the angle , because the two triangles are congruent.
• CThe angle is bigger than the angle , because the two triangles are congruent.
• DThe angles have different measure, because the two triangles are different measure.

Q13:

The figure shows triangles and .

Are the two triangles congruent?

• Ayes
• Bno

• ATriangle can be reflected onto triangle and, thus, the triangles are congruent.
• BTriangle can be translated onto triangle and, thus, the triangles are congruent.
• CNo sequence of translations, reflections, or rotations exists that can map triangle onto triangle and, therefore, the two triangles cannot be congruent.
• DTriangle can be rotated onto triangle and, thus, the triangles are congruent.

Q14:

The figure shows triangles and .

Are the two triangles congruent?

• Ayes
• Bno

• ATriangle can be rotated onto triangle and, thus, the triangles are congruent.
• BTriangle can be translated onto triangle and, thus, the triangles are congruent.
• CNo sequence of translations, reflections, or rotations exists that can map triangle onto triangle and, therefore, the two triangles cannot be congruent.
• DTriangle can be reflected onto triangle and, thus, the triangles are congruent.

Q15:

The figure shows triangles and .

Are the two triangles congruent?

• Ayes
• Bno

• ATriangle can be rotated onto triangle and, thus, the triangles are congruent.
• BTriangle can be translated onto triangle and, thus, the triangles are congruent.
• CNo sequence of translations, reflections, or rotations exists that can map triangle onto triangle and, therefore, the two triangles cannot be congruent.
• DTriangle can be reflected onto triangle and, thus, the triangles are congruent.

Q16:

From the following figure, what can we conclude about a possible Side-Side-Angle (SSA) congruence criterion?

• A SSA is a criterion that works sometimes.
• B SSA is a valid congruence criterion.
• C There is nothing we can conclude.
• D SSA is not a valid congruence criterion.

Q17:

The figure shows triangles and .

Are the two triangles congruent?

• Ayes
• Bno

• ATriangle can be reflected onto triangle and, thus, the triangles are congruent.
• BNo sequence of translations, reflections, or rotations exists that can map triangle onto triangle and, therefore, the two triangles cannot be congruent.
• CTriangle can be rotated onto triangle and, thus, the triangles are congruent.
• DTriangle can be translated onto triangle and, thus, the triangles are congruent.

Q18:

The figure shows triangles and .

Are the two triangles congruent?

• Ano
• Byes