Worksheet: Congruence of Triangles: SSS and SAS Criteria

In this worksheet, we will practice proving that two triangles are congruent using either the SSS or the SAS criterion.

Q1:

Determine whether the triangles in the given figure are congruent, and, if they are, state which of the congruence criteria proves this.

  • A congruent, SSS
  • B congruent, ASA
  • C not congruent
  • D congruent, SAS

Q2:

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

  • A yes
  • B no

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.

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

Q4:

Can you use SAS 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.

Q5:

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

  • A ASA
  • B SAS
  • C SSS

Q6:

In the given quadrilateral, 𝐴 𝐹 and 𝐵 𝐹 have the same length and 𝐸 𝐹 and 𝐶 𝐹 have the same length.

Which angle has the same measure as 𝐴 𝐹 𝐸 ?

  • A 𝐸 𝐹 𝐶
  • B 𝐴 𝐹 𝐵
  • C 𝐴 𝐸 𝐹
  • D 𝐵 𝐹 𝐶
  • E 𝐹 𝐴 𝐸

Hence, are the triangles 𝐴 𝐹 𝐸 and 𝐵 𝐹 𝐶 congruent? If yes, state which congruence criteria proves this.

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

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 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.

Q9:

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

  • A no
  • B yes

Q10:

Determine whether the triangles in the given figure are congruent, and, if they are, state which of the congruence criteria proves this.

  • A Congruent, ASA
  • B Congruent, SAS
  • C Not congruent
  • D Congruent, SSS

Q11:

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

  • A 𝐴 𝑆 𝐴
  • B 𝑆 𝑆 𝑆
  • C 𝑆 𝐴 𝑆

Q12:

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

  • A SAS
  • B ASA
  • C SSS

Q13:

The figure shows triangles 𝐴 𝐵 𝐶 and 𝐷 𝐸 𝐹 .

Are the two triangles congruent?

  • Ayes
  • Bno

Justify your answer with one of the following reasons.

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

Q14:

The figure shows triangles 𝐴 𝐵 𝐶 and 𝐷 𝐸 𝐹 .

Are the two triangles congruent?

  • Ayes
  • Bno

Justify your answer with one of the following reasons.

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

Q15:

The figure shows triangles 𝐴 𝐵 𝐶 and 𝐷 𝐸 𝐹 .

Are the two triangles congruent?

  • Ayes
  • Bno

Justify your answer with one of the following reasons.

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

Are the two triangles congruent?

  • Ayes
  • Bno

Justify your answer with one of the following reasons.

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

Q18:

The figure shows triangles 𝐴 𝐵 𝐶 and 𝐷 𝐸 𝐹 .

Are the two triangles congruent?

  • Ano
  • Byes

Justify your answer with one of the following reasons.

  • ATriangle 𝐴 𝐵 𝐶 can be rotated to obtain triangle 𝐹 𝐸 𝐷 and, thus, the triangles are congruent.
  • BWe can apply a two-stage transformation on triangle 𝐴 𝐵 𝐶 involving a translation and then a rotation to obtain triangle 𝐹 𝐸 𝐷 and, thus, the triangles are congruent.
  • CWe can apply a two-stage transformation on triangle 𝐴 𝐵 𝐶 involving a reflection and then a translation to obtain triangle 𝐹 𝐸 𝐷 and, thus, the triangles are congruent.
  • DNo sequence of translations, reflections, or rotations exists that can map triangle 𝐴 𝐵 𝐶 onto triangle 𝐹 𝐸 𝐷 and, therefore, the two triangles cannot be congruent.

Q19:

The two triangles in the given figure have two sides and a contained angle that are equal. Triangle 𝐴 𝐵 𝐶 could be mapped to triangle 𝐷 𝐸 𝐹 by a reflection in the line 𝐺 𝐻 . Are the two triangles congruent?

  • A yes
  • B no

Q20:

Draw a triangle 𝑋 𝑌 𝑍 which is right angled at 𝑌 and has 𝑋 𝑌 = 𝑌 𝑍 = 4 . Bisect 𝑋 𝑍 at 𝐿 and draw 𝑌 𝐿 . Find 𝑚 𝑋 𝐿 𝑌 .

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