Question

1. consider the three segments shown below such that $overline{ca}$ is congruent to $overline{ab}$ and $overline{ab}$ is congruent to $overline{bd}$. find the missing reason in the proof given.

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step | reason

1. $ca = bd$ | given
2. $ab = ab$ | reflexive property of equality
3. $ca+ab = cb$, $bd + ab=ad$ | segment addition postulate
4. $ca + ab=ab + bd$ |
5. $cb = ad$ | substitution property of equality

q.e.d.

Explanation:

Step1: Recall given equalities

Given $CA = BD$ and from step 3 we have expressions $CA+AB$ and $AB + BD$.

Step2: Apply substitution

Since $CA = BD$, we can substitute $BD$ for $CA$ in the expression $CA+AB$ to get $AB + BD$. So the reason for step 4 is the Substitution Property of Equality.

Answer:

Substitution Property of Equality