Question

Question What reason justifies the answer to the previous question? Given: M is the midpoint of Modifying above A B with bar.. Prove: 2 left-parenthesis A M right-parenthesis equals A B Statements Reasons M is the midpoint of Modifying above A B with bar. given Modifying above A M with bar congruent to Modifying above M B with bar A midpoint divides a segment into two congruent segments. A M equals M B Congruent segments have equal lengths. The length of A M plus the length of M B equals the length of A B Segment Addition Postulate. ? ? 2 left-parenthesis A M right-parenthesis equals A B Combine like terms.(1 point) Responses Distributive Property Distributive Property Symmetric Property of Equality Symmetric Property of Equality Substitution Property of Equality Substitution Property of Equality Subtraction Property of Equality

Answer 1

Answer: To justify the answer that 2(A M) = A B, we can follow the given statements and reasons provided.

1. Given: M is the midpoint of A B

Reason: This is given.

2. Modifying above A M with bar is congruent to Modifying above M B with bar

Reason: A midpoint divides a segment into two congruent segments.

3. A M = M B

Reason: Congruent segments have equal lengths.

4. The length of A M plus the length of M B equals the length of A B

Reason: This is the Segment Addition Postulate.

Therefore, by using the given statements and reasons, we can conclude that 2(A M) = A B.

In summary:

- The midpoint M divides segment A B into two congruent segments, A M and M B.

- Since A M and M B are congruent, they have equal lengths.

- According to the Segment Addition Postulate, the sum of the lengths of A M and M B is equal to the length of A B.

- Therefore, we can justify the answer that 2(A M) = A B.