Question
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
△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
Answers
GPT-4o mini
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.
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.