Question

1. segments dc, ac, and ab are shown in the accompanying figure. it is known that dc is congruent to ab. describe the statement in step 3 of the proof.

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step reason

1. bc ≅ de given
2. bc = de
3. ab + bc = ac segment addition postulate
4. ab + de = ac substitution property of equality

q.e.d.

Explanation:

The Segment - Addition Postulate states that if we have three collinear points \(A\), \(B\), and \(C\), then the length of the whole segment \(AC\) is equal to the sum of the lengths of the two smaller segments \(AB\) and \(BC\). In the context of the proof, since \(A\), \(B\), and \(C\) are collinear points on a line segment, the statement \(AB + BC=AC\) is a direct application of this postulate.

Answer:

The statement in step 3, \(AB + BC = AC\), is based on the Segment - Addition Postulate which says that for collinear points \(A\), \(B\), and \(C\), the length of segment \(AC\) is the sum of the lengths of segments \(AB\) and \(BC\).