Final answer:
Without the context of the proof, it's not possible to select the correct phrase to complete the statement. Each provided option refers to a different set of conditions for proving the congruency of triangles in geometry.
Step-by-step explanation:
The question you've asked seems to be part of a Mathematics assignment related to geometric proofs. Unfortunately, without the context of the proof in question, I cannot definitively complete the statement for you. However, I can explain what each phrase represents.
- AAS Postulate: This stands for Angle-Angle-Side, and it is used when we know two angles and a non-included side of a triangle are congruent to two angles and the corresponding non-included side of another triangle.
- HL Postulate: This stands for Hypotenuse-Leg, and it applies to right triangles when the hypotenuse and one leg in one triangle are congruent to the hypotenuse and one leg in another triangle.
- SAS Postulate: This stands for Side-Angle-Side, and it is used when two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.
- SSS Postulate: This stands for Side-Side-Side, and it is used when three sides of one triangle are congruent to three sides of another triangle.
To determine which phrase best completes your proof, consider the information given and see which postulate or theorem can be applied based on the congruent sides and/or angles mentioned in your proof.