# Lesson Worksheet: Congruence of Triangles: SSS, SAS, and RHS Mathematics • 8th Grade

In this worksheet, we will practice proving that two triangles are congruent using either the side-side-side (SSS), the side-angle-side (SAS), or the right angle-hypotenuse-side (RHS) criterion.

Q1:

Determine whether the triangles in the given figure are congruent, and, if they are, state which of the congruence criteria proves this. • Acongruent, ASA
• Bcongruent, SAS
• Ccongruent, SSS
• Dnot congruent

Q2:

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

• AYes
• BNo

Q3:

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. • ANo
• BYes, SAS
• CYes, ASA
• DYes, SSS

Q4:

Can you use SAS to prove the triangles in the given figure are congruent? Please state your reason. • ANo, because the angle must be contained between the two sides.
• BYes, because there are two pairs of corresponding sides equal in length and one pair of equal angles.

Q5:

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

Q6:

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, SAS
• DYes, SSS

Q7:

State whether the figures are congruent or not congruent. • Acongruent
• Bnot congruent

Q8:

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

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

Q9:

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

Q10:

Determine whether the triangles in the given figure are congruent, and, if they are, state which of the congruence criteria proves this. • ACongruent, ASA
• BCongruent, SSS
• CCongruent, SAS
• DNot congruent

Q11:

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

Q12:

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? • ASSS
• BASA
• CSAS

Q13:

The figure shows triangles and . Are the two triangles congruent?

• AYes
• BNo

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

• ANo
• BYes

• ATriangle can be rotated 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 reflected onto triangle and, thus, the triangles are congruent.
• DTriangle can be translated 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? • ASSA is a criterion that works sometimes.
• BThere is nothing we can conclude.
• CSSA is a valid congruence criterion.
• DSSA 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?

• AYes
• BNo

• ANo sequence of translations, reflections, or rotations exists that can map triangle onto triangle and, therefore, the two triangles cannot be congruent.
• BWe can apply a two-stage transformation on triangle involving a translation and then a rotation to obtain triangle and, thus, the triangles are congruent.
• CTriangle can be rotated to obtain triangle and, thus, the triangles are congruent.
• DWe can apply a two-stage transformation on triangle involving a reflection and then a translation to obtain triangle and, thus, the triangles are congruent.

Q19:

The two triangles in the given figure have two sides and a contained angle that are equal. Triangle could be mapped to triangle by a reflection in the line . Are the two triangles congruent? • Ayes
• Bno

Q20:

Draw a triangle which is right angled at and has . Bisect at and draw . Find .

Q21:

Complete the sentence: These figures are . • Aneither similar nor congruent
• Bsimilar but not congruent
• Ccongruent

Q22:

The two triangles in the given figure have equal sides. Are the two triangles congruent? • AYes
• BNo

Q23:

The diagonal of the rectangle divides its surface into two triangles. 