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
From the given true statements, we can conclude the following:
1. RS + QS = SR - This statement is FALSE. The correct statement should be SR = RS + QS.
2. QR + QS = RS - This statement is FALSE. The correct statement should be QR + QS = SQ.
3. QR + RS = QS - This statement is FALSE. The correct statement should be QS = QR + RS.
4. SQ + RS = QR - This statement is FALSE. The correct statement should be QR = SQ + RS.
Based on the given true statements:
1. RS + QS = SR: This statement is not necessarily true. The correct equation would be SR = QS + RS.
2. QR + QS = RS: This statement is not necessarily true. The correct equation would be RS = QR + QS.
3. QR + RS = QS: This statement is not necessarily true. The correct equation would be QS = QR + RS.
4. SQ + RS = QR: This statement is not necessarily true. The correct equation would be QR = SQ + RS.
In summary, none of the given statements can be concluded to be true based solely on the initial information provided.
To determine what can be concluded from the given true statements, we can apply logic and use our understanding of collinear points.
The statement "Points A, B, and C are collinear, and B is between A and C" implies that the points A, B, and C lie on a straight line, and B is located between A and C.
1. RS + QS = SR: This statement is incorrect. The order of addition should be strictly maintained when adding segments. In this case, the sum of segments RS and QS should be equal to the entire segment SR, not the other way around.
2. QR + QS = RS: This statement is incorrect. The order of addition does not correspond to any known relationships between the given points.
3. QR + RS = QS: This statement is also incorrect. The order of addition does not correspond to any known relationships between the given points.
4. SQ + RS = QR: This statement is correct. According to the properties of collinear points, if B is between A and C, then the sum of segment AB (or BA) and segment BC (or CB) will be equal to the entire segment AC (or CA). So, in this case, we can conclude that SQ + RS = QR.
In summary, the only correct statement among the given options is option 4: SQ + RS = QR.