which reason justifes step 5? Sas, SSS,ASA,AAS
The reason that justifies Step 5 is the Angle-Angle-Side (AAS) congruence postulate.
The justification for step 5, which involves proving congruence using different combinations of angle-side-angle (ASA), angle-angle-side (AAS), or side-angle-side (SAS), will depend on the specific problem or congruence statement being proven.
Briefly, here is how each of these justifications can be used:
1. SAS (Side-Angle-Side): If you have two pairs of corresponding sides that are congruent, and an angle between them that is also congruent, then you can use the SAS congruence theorem to prove that the two triangles are congruent.
2. SSS (Side-Side-Side): If you have three pairs of corresponding sides that are congruent, then you can use the SSS congruence theorem to prove that the two triangles are congruent.
3. ASA (Angle-Side-Angle): If you have two pairs of congruent angles and a pair of congruent sides included between these angles, then you can use the ASA congruence theorem to prove that the two triangles are congruent.
4. AAS (Angle-Angle-Side): If you have two pairs of congruent angles and a pair of corresponding non-included sides that are congruent, then you can use the AAS congruence theorem to prove that the two triangles are congruent.
Again, the specific reason for step 5 will depend on the given information and congruence statement involved in the problem at hand.
The reason that justifies Step 5 in a geometric proof depends on the specific proof you are working with. However, in the context of congruent triangles, Step 5 is often justified using one of the congruence postulates or theorems.
Let's briefly look at each of the congruence postulates/theorems you mentioned and how they relate to Step 5:
1. SAS (Side-Angle-Side) Postulate: This postulate 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. If you are using SAS to justify Step 5, it means that you have shown two sides and the included angle of the triangles are congruent, leading to the justification of their congruence.
2. SSS (Side-Side-Side) Postulate: This postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. If you are using SSS to justify Step 5, it means that you have shown all three sides of the triangles are congruent, leading to the justification of their congruence.
3. ASA (Angle-Side-Angle) Theorem: This 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. If you are using ASA to justify Step 5, it means that you have shown two angles and the included side of the triangles are congruent, leading to the justification of their congruence.
4. AAS (Angle-Angle-Side) Theorem: This 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 triangles are congruent. If you are using AAS to justify Step 5, it means that you have shown two angles and a non-included side of the triangles are congruent, leading to the justification of their congruence.
In conclusion, the reason that justifies Step 5 in a geometric proof could be any of these congruence postulates or theorems, depending on the given information and what you have already proven in the earlier steps of the proof.