ACT Prep: Estimating Line Segment Lengths

The Triangle Inequality Theorem states that in any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

To find the total length of collinear line segments, simply add the lengths of the segments together.

The length of a line segment with endpoints (x1, y1) and (x2, y2) is given by the formula: $$\text{Length} = \text{sqrt}((x2 - x1)^2 + (y2 - y1)^2)$$ .

The length of $$XZ$$ is 21 cm, calculated as $$XZ = XY + YZ = 9 + 12 = 21 cm$$ .

If two line segments are parallel, their lengths can be compared, but they do not affect each other's lengths directly.

Add the lengths of the two segments together to find the total length of the line segment.

The length of $$FG$$ is 24 cm, calculated as $$FG = 3 * DE = 3 * 8 = 24 cm$$ .

Collinearity of points means that the points lie on the same straight line, which affects how we calculate distances between them.

In a triangle, the length of a line segment can be found using the Triangle Inequality Theorem, ensuring that the sum of the lengths of any two sides is greater than the third.

The length of $$MO$$ is 25 cm, calculated as $$MO = MN + NO = 11 + 14 = 25 cm$$ .