Question

Which congruency theorem can be used to prove that △ABD≅△ADC?

a) SSS
b) ASA
c) SAS
d) AAS

Answer 1

Without specific details on the measurements or relationships of sides and angles in triangles △ABD and △ADC, it is not possible to determine the exact congruency theorem. The SSS, ASA, SAS, and AAS theorems all provide various criteria for triangle congruence.

Step-by-step explanation:

The congruency theorem that can be used to prove that △ABD≅△ADC has not been provided with sufficient information to accurately determine a specific theorem. However, I will explain the four congruency theorems mentioned:

1. SSS (Side-Side-Side) Congruence Theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
2. ASA (Angle-Side-Angle) Congruence 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 two triangles are congruent.
3. SAS (Side-Angle-Side) Congruence 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 two triangles are congruent.
4. AAS (Angle-Angle-Side) Congruence Theorem states that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

Without additional information, such as the measurements of the sides and angles of the triangles, it is impossible to determine which theorem applies directly to △ABD and △ADC.