Question

1. in the figure, points l, m, and n lie on the segment kp. what is the missing reason for the statement in step 4 of the proof?

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step reason

1. $overline{ae}congoverline{cd}$ given
2. $ae = cd$ definition of congruent segments
3. $ae + eb = ab$ segment addition postulate
4. $cd + eb = ab$

q.e.d.

Explanation:

In step 2, we have $AE = CD$. In step 3, we have $AE+EB = AB$. By substituting $AE$ with $CD$ (since they are equal), we get $CD + EB=AB$ in step 4. This is based on the Substitution Property of Equality which states that if $a = b$, then $a$ can be replaced by $b$ in any equation or expression.

Answer:

Substitution Property of Equality