Question

suppose that the two parts of the ladder, ac and bd, are the same length (that is, ac = bd). complete the following two statements. 38. because a - b - c, ac = ?. 39. because b - c - d, bd = ?. 40. why is ab + bc = bc + cd? 41. why is ab = cd?

Explanation:

Step1: Understand segment - addition postulate

If A - B - C, then by the segment - addition postulate, $AC=AB + BC$.

Step2: Understand segment - addition postulate for B - C - D

If B - C - D, then by the segment - addition postulate, $BD=BC + CD$.

Step3: Analyze the equality $AB + BC=BC + CD$

Since $AC = BD$ (given) and $AC=AB + BC$, $BD=BC + CD$ (from previous steps), we can substitute to get $AB + BC=BC + CD$.

Step4: Prove $AB = CD$

Subtract $BC$ from both sides of the equation $AB + BC=BC + CD$. Using the subtraction property of equality, $(AB + BC)-BC=(BC + CD)-BC$, which simplifies to $AB = CD$.

Answer:

1. $AB + BC$
2. $BC + CD$
3. Because $AC = BD$, and $AC=AB + BC$, $BD=BC + CD$.
4. By subtracting $BC$ from both sides of the equation $AB + BC=BC + CD$.