Question

select the best description for the diagram. (overline{ab}) intersecting (overleftrightarrow{cd}) at point (k), so that (overline{ak} cong overline{kc}) and (overline{bk} cong overline{kd}) (overline{ab}) intersecting (overleftrightarrow{cd}) at point (k), so that (overline{ak} cong overline{kd}) and (overline{bk} cong overline{kc}) (overline{ab}) intersecting (overleftrightarrow{cd}) at point (k), so that (overline{ak} cong overline{kb}) and (overline{ck} cong overline{kd}) (overleftrightarrow{ab}) intersecting (overleftrightarrow{cd}) at point (k), so that (overline{ak} cong overline{kb}) and (overline{ck} cong overline{kd})

Explanation:

1. Analyze the diagram: $\overline{AB}$ is a segment (not a line, as it has endpoints A and B), and $\overleftrightarrow{CD}$ is a line. They intersect at K.
2. Check congruency: Marks show $AK \cong KB$ (since $\overline{AB}$ has two marks on each side of K) and $CK \cong KD$ (since $\overleftrightarrow{CD}$ has one mark on each side of K).
3. Evaluate options:

• First option: $AK \cong KC$ is false (different mark counts).
• Second option: $AK \cong KD$ and $BK \cong KC$ are false (mismatched segments).
• Third option: Correctly identifies $\overline{AB}$ intersecting $\overleftrightarrow{CD}$ at K, with $AK \cong KB$ and $CK \cong KD$.
• Fourth option: $\overleftrightarrow{AB}$ is incorrect (AB is a segment, not a line).

Answer:

$\boldsymbol{\overline{AB}}$ intersecting $\boldsymbol{\overleftrightarrow{CD}}$ at point $K$, so that $\boldsymbol{\overline{AK} \cong \overline{KB}}$ and $\boldsymbol{\overline{CK} \cong \overline{KD}}$ (the third option)