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Worksheet: Proving Triangles' Congruence Using ASA and AAS Criterions

Q1:

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

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

  • Ayes
  • Bno

Q3:

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

  • Ano
  • Byes

Q4:

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

  • Anot congruent
  • Bcongruent,
  • Ccongruent,
  • Dcongruent,

Q5:

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

  • Ano
  • Byes,
  • Cyes,
  • Dyes,

Q6:

Can you use 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

Q7:

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

  • Anot congruent
  • Bcongruent,
  • Ccongruent,
  • Dcongruent,

Q8:

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

  • ASSS
  • BASA
  • CSAS

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, SAS
  • Cyes, ASA
  • Dyes, SSS

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,
  • Byes,
  • Cyes,
  • Dno

Hence, what can we conclude about the angles and ?

  • AWe cannot conclude anything, because we need more information.
  • BThe angle is bigger than the angle , because the two triangles are congruent.
  • CThe angles have the same measure, because the triangles are congruent
  • DThe angle is bigger than the angle , because the two triangles are congruent.
  • EThe angles have different measure, because the two triangles are different measure.

Q13:

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

Q15:

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

Q16:

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

  • AThere is nothing we can conclude.
  • BSSA is the same as SSA.
  • CSSA is not a valid congruence criterion.
  • DSSA is a criterion that works sometimes.
  • ESSA is 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.
  • 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.

Q18:

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 to obtain 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.
  • CWe can apply a two-stage transformation on triangle involving a translation and then a rotation 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.