Question

use the number line to answer the question.
a b c d
-4 -3 -2 -1 0 1 2 3 4
which two line segments are congruent?
list the two segments separated by a comma.
segments

Explanation:

Step1: Calculate the length of segment \(AB\)

The coordinate of \(A\) is \(-4\) and the coordinate of \(B\) is \(-2\). The length of \(AB\) is \(|-2 - (-4)|=|-2 + 4| = 2\).

Step2: Calculate the length of segment \(BC\)

The coordinate of \(B\) is \(-2\) and the coordinate of \(C\) is \(-1\). The length of \(BC\) is \(|-1-(-2)|=|-1 + 2|=1\).

Step3: Calculate the length of segment \(CD\)

The coordinate of \(C\) is \(-1\) and the coordinate of \(D\) is \(2\). The length of \(CD\) is \(|2-(-1)|=|2 + 1| = 3\).

Step4: Calculate the length of segment \(AD\)

The coordinate of \(A\) is \(-4\) and the coordinate of \(D\) is \(2\). The length of \(AD\) is \(|2-(-4)|=|2 + 4|=6\).

Step5: Check congruent segments

Congruent segments have equal lengths.
The length of \(AB\) is \(2\), the length of \(BC\) is \(1\), the length of \(CD\) is \(3\), and the length of \(AD\) is \(6\).
Let's check other possible segments.
The distance from \(-4\) to \(-2\) (segment \(AB\)): \(d_{AB}=|-2-(-4)| = 2\)
The distance from \(-2\) to \(0\) (assuming we consider intervals of length \(2\) in another way, but no, let's re - check.
Wait, another approach: count the number of units between the points.
From \(A(-4)\) to \(B(-2)\): \(|-4-(-2)| = 2\) units.
From \(B(-2)\) to \(C(-1)\): \(|-2-(-1)|=1\) unit.
From \(C(-1)\) to \(D(2)\): \(|2 - (-1)|=3\) units.
From \(A(-4)\) to \(C(-1)\): \(|-1-(-4)|=3\) units. So \(AC\) and \(CD\) are congruent.

Answer:

\(AC,CD\)