# Worksheet: Congruence of Triangles: SSS, SAS, and RHS

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.

**Q2: **

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

- Ayes
- Bno

**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

**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

Justify your answer with one of the following reasons.

- 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

Justify your answer with one of the following reasons.

- 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

Justify your answer with one of the following reasons.

- 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

Justify your answer with one of the following reasons.

- 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

Justify your answer with one of the following reasons.

- 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

**Q24: **

State whether the figures are congruent or not congruent.

- Acongruent
- Bnot congruent