Free Line & angle proofs Practice Problems • Learn To Be

\overleftrightarrow{AB}

and

\overleftrightarrow{DE}

are parallel lines.

Perform a translation that proves corresponding angles are always equal and select the option which explains the proof.

Choose 1 answer:

A
Since the image of a line under a translation is parallel to the original line, the translation that maps point $D$ to point $B$ also maps $\angle{CDF}$ to $\angle{ABD}$ . Translations preserve angle measures, so $\green{x}=\pink{y}$ .
B
The translation that maps point $D$ to point $E$ produces a parallelogram. Therefore, $\green{x}=\pink{y}$ .
C
The translation mapping point $F$ to point $D$ produces a new line which is a bisector of segment $\overline{DB}$ . Constructing the bisector in the presence of parallel lines $\overleftrightarrow{AB}$ and $\overleftrightarrow{DE}$ proves that $\green{x}=\pink{y}$ .

Line & angle proofs