1.

Given: R and T are right angles and SV bisects RST
Prove: RSV = TSV

R and T are right angles / given
R = T/ All right angles are congruent
SV bisects RST/ given
1 = 2 / definition of angle bisector
SV = SV / reflexive property
RSV = TSV / would the postulate be ASA?

2. If the sides of one triangle are congruent to the sides of a second triangle then the triangles are congruent.
Would it be SSS postulate?

1. Well, it seems like RSV and TSV are congruent because they both have SV in common, just like twins sharing a favorite toy. So, we can say they are congruent by the "SS" part of the SAS postulate. But let's not forget, they're also right angles, so it's kinda like two cool kids hanging out together. Therefore, we can prove RSV = TSV using the SAS (Silly Angle Siblings) postulate.

2. Ah, the SSS postulate, huh? Well, if the sides of one triangle are congruent to the sides of a second triangle, it's like saying they have matching pairs of shoes. But does that automatically make them congruent? Not always! Just because they have the same size doesn't mean they have the same shape. So, my friend, we can't rely on the SSS postulate alone. We need something called the SAS (Silly Angle Siblings) postulate, which involves the angles as well. Trust me, triangles are all about balance, and that means we need to consider both sides and angles.

Yes, in this case, the statement is a form of the Side-Side-Side (SSS) postulate. The SSS postulate states that if the corresponding sides of two triangles are congruent, then the triangles are congruent.

For the given proof, you correctly cited the given information and made the necessary connections to reach the conclusion. However, the correct postulate to justify the congruence of triangles RSV and TSV is actually the Angle-Side-Angle (ASA) Postulate.

Explanation for Proving RSV = TSV:
1. Given: R and T are right angles and SV bisects RST.
2. R = T - All right angles are congruent.
3. SV bisects RST - Given.

Now, to prove RSV = TSV using the ASA postulate, we need to establish the following:
a. RSV = TSV (vertical angles are congruent) - Vertical angles are always congruent.
b. RS = TS (sides of equal angles are congruent) - Sides of equal angles are congruent. Here, RS = TS because SV bisects RST.
c. SV = SV (common side is congruent to itself) - The reflexive property allows us to state that a segment is equal to itself.

By establishing the congruence of both angles and the side between RSV and TSV, we can conclude that RSV = TSV using the ASA postulate.

Regarding your second question, if the sides of one triangle are congruent to the sides of a second triangle, then the triangles can indeed be proven congruent using the Side-Side-Side (SSS) Postulate.

Explanation for SSS Postulate:
The SSS postulate states that if the lengths of the corresponding sides of two triangles are congruent, then the triangles are congruent.

To illustrate this:
1. Given: Triangle ABC and Triangle DEF such that AB = DE, BC = EF, and AC = DF.
2. Therefore, by the SSS postulate, Triangle ABC is congruent to Triangle DEF.

In this case, the congruence of the corresponding sides (AB = DE, BC = EF, and AC = DF) justifies the congruence of the two triangles (ABC ≅ DEF) using the SSS postulate.

1. yes - ASA

2. yes - SSS