For the given true statements, what can you conclude? If points A, B, and C are collinear, and B is between A and C, then AB + BC = AC. Points Q, R, and S are collinear and R is between Q and S. 1 RS + QS = SR 2 QR + QS = RS 3 QR + RS = QS 4 SQ + RS = QR
For the given true statements:
1) If points A, B, and C are collinear, and B is between A and C, then AB + BC = AC.
Based on this statement, we can conclude that AB + BC = AC.
2) Points Q, R, and S are collinear and R is between Q and S.
By this statement, we know that R is between Q and S, which means that RQ + QS = RS.
Therefore, the conclusions we can make are:
1) AB + BC = AC
2) RQ + QS = RS
From the given true statements, we can conclude:
1) RS + QS = SR (This statement is redundant and not meaningful, as addition is commutative)
2) QR + QS = RS (This statement is not true because in a valid equation with collinear points, the two segments being added should add up to the segment they are a part of)
3) QR + RS = QS (This statement is not true because in a valid equation with collinear points, the two segments being added should add up to the segment they are a part of)
4) SQ + RS = QR (This statement is true because in a valid equation with collinear points and segment addition, the two segments being added should add up to the segment they are a part of, which is consistent with the statement provided)
To determine what can be concluded from the given true statements, let's break down each statement and analyze them one by one:
Statement 1: RS + QS = SR
This statement is not necessarily true. The order of the points matters when considering segments. The correct statement should be SR + RQ = RS. Therefore, we cannot conclude anything from this statement.
Statement 2: QR + QS = RS
This statement is also not necessarily true. Again, the order matters, and the correct statement should be QS + SR = QR. Therefore, we cannot conclude anything from this statement either.
Statement 3: QR + RS = QS
This statement is not true. According to the given true statements, B is between A and C. Therefore, AB + BC = AC, not QR + RS = QS. We cannot conclude anything from this statement.
Statement 4: SQ + RS = QR
This statement is also not true. Similar to the previous statement, QR + RS = QS is not the correct statement. Hence, we cannot conclude anything from this statement either.
In summary, we cannot draw any valid conclusions from the given true statements. It is important to carefully analyze the given statements and definitions to determine their validity and draw accurate conclusions.