Congruent Triangles Criteria

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Questions and Answers

If three sides of one triangle are equal to three sides of another triangle, what can be concluded about the triangles?

  • The triangles have same perimeter.
  • The triangles are congruent. (correct)
  • The triangles are similar.
  • The triangles are right-angled.

Which of the following is not a criterion for congruent triangles?

  • AAA Criterion (correct)
  • SAS Criterion
  • ASA Criterion
  • SSS Criterion

If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, what can be concluded about the triangles?

  • The triangles have same perimeter.
  • The triangles have same area.
  • The triangles are congruent. (correct)
  • The triangles are similar.

If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, what can be concluded about the triangles?

<p>The triangles are congruent. (C)</p> Signup and view all the answers

If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, what can be concluded about the triangles?

<p>The triangles are congruent. (D)</p> Signup and view all the answers

Which criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent?

<p>SAS Criterion (C)</p> Signup and view all the answers

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Study Notes

Congruent Triangles

Criteria for Congruent Triangles

SSS Criterion (Side-Side-Side)

  • If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.
  • This criterion ensures that the corresponding sides of the two triangles are equal.

ASA Criterion (Angle-Side-Angle)

  • If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.
  • The included side is the side between the two given angles.

SAS Criterion (Side-Angle-Side)

  • If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.
  • The included angle is the angle between the two given sides.

AAS Criterion (Angle-Angle-Side)

  • If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.
  • The non-included side is a side that is not between the two given angles.

Note: These criteria are used to prove that two triangles are congruent, and they are all equivalent.

Congruent Triangles

Criteria for Congruent Triangles

SSS Criterion

  • Three sides of one triangle are equal to three sides of another triangle, ensuring corresponding sides are equal.

ASA Criterion

  • Two angles and the included side of one triangle are equal to two angles and the included side of another triangle.
  • The included side is the side between the two given angles.

SAS Criterion

  • Two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
  • The included angle is the angle between the two given sides.

AAS Criterion

  • Two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle.
  • The non-included side is a side that is not between the two given angles.

General Notes

  • These criteria are used to prove that two triangles are congruent.
  • All four criteria (SSS, ASA, SAS, and AAS) are equivalent.

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