Answered

Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Start with the given information.

[tex]\[
\begin{array}{|c|c|c|}
\hline
Step & Statement & Reason \\
\hline
1 & AC = AB + AB & Given \\
\hline
2 & AB + BC = AC & Segment Addition Postulate \\
\hline
3 & AB + BC = AB + AB & Substitution \\
\hline
4 & AB = BC & Subtraction Property \\
\hline
\end{array}
\][/tex]

Sagot :

GinnyAnswer
Let's work through the given information step-by-step and develop a clear solution:

[tex]\[ \begin{tabular}{|c|c|c|} \hline Step & Statement & Reason \\ \hline 1 & AC = AB + AB & Given \\ \hline 2 & AB + BC = AC & Segment Addition Postulate \\ \hline 3 & AB + BC = AB + AB & By substitution of AC from Step 1 in Step 2 \\ \hline 4 & BC = AB & Subtraction Property (Subtract AB from both sides of Step 3) \\ \hline \end{tabular} \][/tex]

After completing these steps, we can deduce the following:

1. We know from the given information that [tex]\( AC = AB + AB \)[/tex].
2. According to the Segment Addition Postulate, [tex]\( AB + BC = AC \)[/tex]. This means that the sum of the lengths of the segments [tex]\( AB \)[/tex] and [tex]\( BC \)[/tex] is equal to the length of [tex]\( AC \)[/tex].
3. By substituting [tex]\( AC \)[/tex] from Step 1 into Step 2, we get: [tex]\( AB + BC = AB + AB \)[/tex].
4. By subtracting [tex]\( AB \)[/tex] from both sides of the equation [tex]\( AB + BC = AB + AB \)[/tex], we find [tex]\( BC = AB \)[/tex].

So, we have two key conclusions:

- [tex]\( AB = BC \)[/tex] (derived using the Subtraction Property).
- From the above equality, if we substitute [tex]\( BC \)[/tex] with [tex]\( AB \)[/tex] in the initial statement [tex]\( AC = AB + AB \)[/tex], we maintain the relationship [tex]\( AC = AB + AB \)[/tex].

These relationships clarify:
- [tex]\( AB = BC \)[/tex] (segment equality).
- Since [tex]\( AC = AB + AB \)[/tex] can also be expressed as [tex]\( AC = 2AB \)[/tex] and we derived [tex]\( AB = BC \)[/tex]; hence, the length of [tex]\( AC \)[/tex] is twice the length of [tex]\( AB \)[/tex], and since [tex]\( AB = BC \)[/tex], the result [tex]\( AC = BC \)[/tex] holds naturally due to the equality [tex]\( AB = BC \)[/tex].
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.