Question

question 4 | module 3 quiz(3.4 - 3.6)
a b c d
complete the proof
statements reasons

1. \\(\overline{ab}\cong\overline{cd}\\) 1. given
2. \\(ab = cd\\) 2. definition of congruence
3. \\(ab + bc=bc + cd\\) 3. select choice
4. \\(ab + bc = ac, bc+cd = bd\\) 4. select choice
5. \\(ac = bd\\) 5. substitution
6. \\(\overline{ac}\cong\overline{bd}\\) 6. definition of congruence

Explanation:

Step1: Add BC to both sides

If \(a = b\), then \(a + c=b + c\). Here \(a = AB\), \(b = CD\) and \(c = BC\), so \(AB+BC = BC + CD\) by the Addition Property of Equality.

Step2: Segment - addition postulate

The sum of two adjacent segments on a line gives the total length of the combined segment. So \(AB + BC=AC\) and \(BC + CD = BD\) by the Segment - Addition Postulate.

Answer:

1. Addition Property of Equality
2. Segment - Addition Postulate