Question

select the correct answer from each drop - down menu.
given: $overline{ac} cong overline{xz}$, $overline{bc} cong overline{xy}$
prove: $overline{ab} cong overline{yz}$
complete the proof.
suppose $overline{ab}
otcong overline{yz}$. by the definition of congruence, $ab
eq yz$. by the addition property of equality, $ab + bc
eq yz + bc$. using the given, $bc = xy$ because of the definition of congruence. applying the substitution property of equality, $ab + bc
eq yz + xy$. applying segment addition to $ab + bc
eq yz + xy$, . however, we are given that $overline{ac} cong overline{xz}$, which implies $ac = xz$ by the definition of congruence.

Explanation:

This is a proof by contradiction. We start by assuming $\overline{AB}
cong \overline{YZ}$, so $AB
eq YZ$. After substituting the given congruent segments, we use the segment addition postulate: $AB + BC = AC$ and $YZ + XY = XZ$. Substituting these into the inequality gives $AC
eq XZ$, which directly contradicts the given $\overline{AC} \cong \overline{XZ}$ (meaning $AC = XZ$). The missing statement is the contradiction that arises from the assumption.

Answer:

AC does not equal XZ