COMPARING SEGMENTS In Exercises 33 and 34, the endpoints of...

COMPARING SEGMENTS In Exercises 33 and 34, the endpoints of two segments are given. Find each segment length. Tell whether the segments are congruent. If they are not congruent, state which segment length is greater $$ \overline{\mathrm{AB}} : \mathrm{A}(0,2), \mathrm{B}(-3,8) \text { and } \overline{\mathrm{CD}} : \mathrm{C}(-2,2), \mathrm{D}(0,-4) $$

COMPARING SEGMENTS In Exercises 33 and 34, the endpoints of two segments are given. Find each segment length. Tell whether the segments are congruent. If they are not congruent, state which segment length is greater
$$
\overline{\mathrm{AB}} : \mathrm{A}(0,2), \mathrm{B}(-3,8) \text { and } \overline{\mathrm{CD}} : \mathrm{C}(-2,2), \mathrm{D}(0,-4)
$$

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Key Concepts

Distance Formula

The distance formula is a mathematical expression used to calculate the length of a segment between two points in the coordinate plane. It is derived from the Pythagorean theorem and involves taking the square root of the sum of the squares of the differences in the x-coordinates and the y-coordinates of the points.

Line Segment

A line segment is a part of a line that is bounded by two distinct endpoints. Its length can be determined by applying the distance formula to the coordinates of these endpoints.

Segment Congruence

Segment congruence in geometry refers to the condition where two segments have the exact same length. When comparing segments, one determines if they are congruent by calculating and comparing their lengths using a consistent measurement method, such as the distance formula.

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