Question

1. complete a two - column proof. you should not need all the lines. (it took me about 4 lines to complete this proof.) look at the last proof we did in class! 2. a b c d given: ab = cd prove: ac = bd statements reasons 1. ab = cd 1. given 2. 2. 3. 3. 4. 4. 5. 5. 6. 6. 7. 7.

Explanation:

Step1: Identify common segment

$BC$ is common to both $AC$ and $BD$.

Step2: Express $AC$ and $BD$ in parts

$AC=AB + BC$ and $BD=CD + BC$.

Step3: Substitute using given

Since $AB = CD$ (given), we substitute $AB$ for $CD$ in the expression for $BD$. So $BD=AB + BC$.

Step4: Conclude equality

Since $AC=AB + BC$ and $BD=AB + BC$, we have $AC = BD$.

Answer:

Statements	Reasons
2. $AC=AB + BC$; $BD=CD + BC$	2. Segment - addition postulate
3. $BD=AB + BC$	3. Substitution property (because $AB = CD$)
4. $AC = BD$	4. Transitive property