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Worksheet: Proving Triangles' Congruence Using SSS and SAS Criteria

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 𝐴 𝐡 𝐢 and triangle 𝐡 𝐢 𝐷 have two equal sides and share one equal angle. Are triangles 𝐴 𝐡 𝐢 and 𝐡 𝐢 𝐷 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, 𝑆 𝑆 𝑆
  • B congruent, 𝐴 𝑆 𝐴
  • C not congruent
  • D congruent, 𝑆 𝐴 𝑆

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 𝑆 𝐴 𝑆 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, 𝐴 𝑆 𝐴
  • B congruent, 𝑆 𝐴 𝑆
  • C not congruent
  • D congruent, 𝑆 𝑆 𝑆

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 𝐴 𝑆 𝐴
  • B 𝑆 𝑆 𝑆
  • C 𝑆 𝐴 𝑆

Q10:

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

  • A 𝑆 𝐴 𝑆
  • B 𝐴 𝑆 𝐴
  • C 𝑆 𝑆 𝑆

Q11:

In the given quadrilateral, 𝐴 𝐹 and 𝐡 𝐹 have the same length and 𝐸 𝐹 and 𝐢 𝐹 have the same length.

Which angle has the same measure as ∠ 𝐴 𝐹 𝐸 ?

  • A ∠ 𝐸 𝐹 𝐢
  • B ∠ 𝐴 𝐹 𝐡
  • C ∠ 𝐴 𝐸 𝐹
  • D ∠ 𝐡 𝐹 𝐢
  • E ∠ 𝐹 𝐴 𝐸

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

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

Q12:

The figure shows triangles 𝐴 𝐡 𝐢 and 𝐷 𝐸 𝐹 .

Are the two triangles congruent?

  • Ayes
  • Bno

Justify your answer with one of the following reasons.

  • ATriangle 𝐴 𝐡 𝐢 can be reflected onto triangle 𝐷 𝐸 𝐹 and, thus, the triangles are congruent.
  • BTriangle 𝐴 𝐡 𝐢 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 𝐡 𝐢 onto triangle 𝐷 𝐸 𝐹 and, therefore, the two triangles cannot be congruent.
  • DTriangle 𝐴 𝐡 𝐢 can be rotated onto triangle 𝐷 𝐸 𝐹 and, thus, the triangles are congruent.

Q13:

The figure shows triangles 𝐴 𝐡 𝐢 and 𝐷 𝐸 𝐹 .

Are the two triangles congruent?

  • Ayes
  • Bno

Justify your answer with one of the following reasons.

  • ATriangle 𝐴 𝐡 𝐢 can be rotated onto triangle 𝐷 𝐸 𝐹 and, thus, the triangles are congruent.
  • BTriangle 𝐴 𝐡 𝐢 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 𝐡 𝐢 onto triangle 𝐷 𝐸 𝐹 and, therefore, the two triangles cannot be congruent.
  • DTriangle 𝐴 𝐡 𝐢 can be reflected onto triangle 𝐷 𝐸 𝐹 and, thus, the triangles are congruent.

Q14:

The figure shows triangles 𝐴 𝐡 𝐢 and 𝐷 𝐸 𝐹 .

Are the two triangles congruent?

  • Ayes
  • Bno

Justify your answer with one of the following reasons.

  • ATriangle 𝐴 𝐡 𝐢 can be rotated onto triangle 𝐷 𝐸 𝐹 and, thus, the triangles are congruent.
  • BTriangle 𝐴 𝐡 𝐢 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 𝐡 𝐢 onto triangle 𝐷 𝐸 𝐹 and, therefore, the two triangles cannot be congruent.
  • DTriangle 𝐴 𝐡 𝐢 can be reflected onto triangle 𝐷 𝐸 𝐹 and, thus, the triangles are congruent.

Q15:

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.

Q16:

The figure shows triangles 𝐴 𝐡 𝐢 and 𝐷 𝐸 𝐹 .

Are the two triangles congruent?

  • Ayes
  • Bno

Justify your answer with one of the following reasons.

  • ATriangle 𝐴 𝐡 𝐢 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 𝐡 𝐢 onto triangle 𝐷 𝐸 𝐹 and, therefore, the two triangles cannot be congruent.
  • CTriangle 𝐴 𝐡 𝐢 can be rotated onto triangle 𝐷 𝐸 𝐹 and, thus, the triangles are congruent.
  • DTriangle 𝐴 𝐡 𝐢 can be translated onto triangle 𝐷 𝐸 𝐹 and, thus, the triangles are congruent.

Q17:

The figure shows triangles 𝐴 𝐡 𝐢 and 𝐷 𝐸 𝐹 .

Are the two triangles congruent?

  • Ano
  • Byes

Justify your answer with one of the following reasons.

  • ATriangle 𝐴 𝐡 𝐢 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 𝐡 𝐢 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 𝐡 𝐢 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 𝐡 𝐢 onto triangle 𝐹 𝐸 𝐷 and, therefore, the two triangles cannot be congruent.

Q18:

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

  • A yes
  • B no

Q19:

Draw a triangle 𝑋 π‘Œ 𝑍 which is right angled at π‘Œ and has 𝑋 π‘Œ = π‘Œ 𝑍 = 4 . Bisect 𝑋 𝑍 at 𝐿 and draw π‘Œ 𝐿 . Find π‘š ∠ 𝑋 𝐿 π‘Œ .