Question

given: ab ≅ cd. prove: ac ≅ bd. note: quadrilateral properties are not permitted in this proof. step 1 statement ab ≅ cd reason given type of statement try answer example: call of a you must answer all questions above in order to submit. since ad is a segment.

Explanation:

Step1: Use segment addition postulate

$$ AC = AB + BC $$

Step2: Use segment addition postulate

$$ BD=BC + CD $$

Step3: Substitute \(AB = CD\) (given)

Since \(AB = CD\), then \(AC=CD + BC\) and \(BD = BC+CD\).

Step4: Conclude

By substitution property, \(AC = BD\), so \(\overline{AC}\cong\overline{BD}\)

Answer:

\(\overline{AC}\cong\overline{BD}\)