Point B is between A and C
Point A is between B and C
Point C is between A and B
Understanding the Segment Addition Postulate
The Segment Addition Postulate is a fundamental concept in Euclidean geometry. It states that if three points A, B, and C are collinear (lie on the same line) and point B is between points A and C, then the length of the segment AC is equal to the sum of the lengths of the segments AB and BC.
Mathematically, this is expressed as:
AC = AB + BC
This postulate is crucial for solving various geometry problems involving line segments. It allows us to find the length of a whole segment if we know the lengths of its constituent parts, or to find the length of a part if we know the whole and the other part.
How This Calculator Works
This calculator simplifies applying the Segment Addition Postulate. You provide the lengths of two segments and specify their arrangement on a line. The calculator then determines the total length of the combined segment based on the postulate.
Scenarios:
Point B is between A and C: This is the standard application. If you input the lengths of AB and BC, the calculator finds AC. For example, if AB = 5.2 and BC = 8.1, then AC = 5.2 + 8.1 = 13.3.
Point A is between B and C: In this case, the entire segment is BC, and it's composed of BA and AC. If you know AB (which is the same as BA) and BC, you can find AC by rearranging the formula: AC = BC - AB. For example, if AB = 5.2 and BC = 13.3, then AC = 13.3 - 5.2 = 8.1.
Point C is between A and B: Similarly, the entire segment is AB, composed of AC and CB. If you know AB and BC (which is the same as CB), you can find AC: AC = AB - BC. For example, if AB = 13.3 and BC = 8.1, then AC = 13.3 - 8.1 = 5.2.
Note: The calculator assumes that the provided lengths are positive values. In geometric contexts, lengths cannot be negative.
Use Cases
The Segment Addition Postulate and this calculator are useful in various educational and practical settings:
Mathematics Education: Teaching and reinforcing basic geometry principles.
Drafting and Design: Calculating lengths for architectural drawings or design plans where components are laid out linearly.
Navigation: Estimating distances when moving along a straight path with intermediate points.
Problem Solving: As a foundational tool for more complex geometric proofs and calculations.
function calculateSegmentLength() {
var segment1Input = document.getElementById("segment1Length");
var segment2Input = document.getElementById("segment2Length");
var pointLocation = document.getElementById("pointLocation").value;
var resultDisplay = document.getElementById("result");
var resultContainer = document.getElementById("resultContainer");
var lengthAB = parseFloat(segment1Input.value);
var lengthBC = parseFloat(segment2Input.value);
var totalLength = NaN;
var displayText = "";
// Input validation
if (isNaN(lengthAB) || isNaN(lengthBC)) {
resultDisplay.textContent = "Please enter valid numbers for segment lengths.";
resultContainer.style.backgroundColor = "#dc3545"; // Red for error
resultContainer.style.display = "block";
return;
}
if (lengthAB < 0 || lengthBC AC = BC – BA
// Note: BA is the same length as AB
if (lengthBC AC = AB – CB
// Note: CB is the same length as BC
if (lengthAB < lengthBC) {
resultDisplay.textContent = "Error: Total length AB must be greater than or equal to segment BC.";
resultContainer.style.backgroundColor = "#dc3545"; // Red for error
resultContainer.style.display = "block";
return;
}
totalLength = lengthAB – lengthBC;
displayText = "Length AC = " + totalLength.toFixed(2);
}
resultDisplay.textContent = displayText;
resultContainer.style.backgroundColor = getComputedStyle(document.documentElement).getPropertyValue('–success-green'); // Reset to green
resultContainer.style.display = "block";
}