Question

prove ( overline{ac} cong overline{bd} )
complete the proof
statements

1. ( ab cong cd )
2. ( ab = cd )
3. ( ab + bc = bc + cd )
4. ( ab + bc = ac, bc + cd = bd )
5. ( ac = bd )
6. ( overline{ac} cong overline{bd} )

reasons

1. given
2. definition of congruence
3. ..................
4. ..................
5. substitution
6. definition of congruence

drag & drop the answer
definition of congruence given substitution addition property of equality segment addition postulate

Explanation:

• For step 3: When we add \(BC\) to both sides of the equation \(AB = CD\) (from step 2 where \(AB = CD\) based on the definition of congruence), we are using the Addition Property of Equality. This property states that if \(a=b\), then \(a + c=b + c\). Here \(a = AB\), \(b = CD\), and \(c=BC\).
• For step 4: The Segment Addition Postulate states that if we have three collinear points \(A\), \(B\), \(C\), then \(AB+BC = AC\), and if we have three collinear points \(B\), \(C\), \(D\), then \(BC + CD=BD\). This is exactly what is being applied in this step.

Answer:

1. Addition Property of Equality
2. Segment Addition Postulate