To determine which theorem proves that triangle ABC is congruent to triangle ABD (△ABC≅△ABD), we need to analyze the characteristics of these triangles based on typical congruence criteria.
- SAS Theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
- SSS Theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
- ASA Theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
- HL Theorem (Hypotenuse-Leg) applies specifically to right triangles.
Without the specific details from the picture you mentioned, I can provide a general guide.
If you can confirm which sides and angles are congruent, you can choose as follows:
- If two sides and the angle between them are congruent, choose SAS.
- If all three sides are congruent, choose SSS.
- If two angles and the side between them are congruent, choose ASA.
- If the triangles are right triangles and you use the hypotenuse and one leg, choose HL.
Please select the theorem based on the specific information presented in the picture regarding the sides and angles of triangles ABC and ABD. If you provide more details or confirm the congruences, I can assist you further!