Ask a New Question
Menu

Question

△ABC≅△ABD
Using the info provided in the picture below, which theorem proves this?

(1 point)
Responses

ASA Theorem
ASA Theorem

SAS Theorem
SAS Theorem

SSS Theorem
SSS Theorem

HL Theorem

1 answer

To determine which theorem proves that \( \triangle ABC \congruent \triangle ABD \), we would typically rely on the information provided in the picture. However, since I cannot see the picture or any specific information about angles or sides, I can give you a brief overview of the theorems:

  1. ASA Theorem (Angle-Side-Angle): States that if in two triangles, two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, then the triangles are congruent.

  2. SAS Theorem (Side-Angle-Side): States that if in two triangles, two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle, then the triangles are congruent.

  3. SSS Theorem (Side-Side-Side): States that if the three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent.

  4. HL Theorem (Hypotenuse-Leg for Right Triangles): Applies specifically to right triangles, stating that if the hypotenuse and one leg of a right triangle is equal to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

To determine which theorem applies, check what specific information is given about the angles and sides between triangles \( ABC \) and \( ABD \):

  • If you know two angles and the included side are equal, use the ASA theorem.
  • If you know two sides and the angle between them is equal, use the SAS theorem.
  • If all three sides are equal, use the SSS theorem.
  • If both triangles are right triangles with equal hypotenuses and one leg, use the HL theorem.

Choose the theorem based on the information provided in the picture.