Free Line & angle proofs Practice Problems • Learn To Be

C

is the point on

\overleftrightarrow{DE}

which is equally distant from lines

\overleftrightarrow{AE}

and

\overleftrightarrow{DB}

.

\overleftrightarrow{AE}

and

\overleftrightarrow{DB}

are parallel lines.

Perform a rotation that proves alternate interior angles are always equal and select the option which best explains the proof.

Choose 1 answer:

A
The $180^\circ$ rotation about $D$ maps $\overleftrightarrow{DB}$ to itself and $\overleftrightarrow{DE}$ to itself. Rotations preserve angle measures, so $\pink u = \green v$ .
B
The $180^\circ$ rotation about $C$ maps $\overleftrightarrow{DB}$ to $\overleftrightarrow{EA}$ and maps $\overleftrightarrow{DE}$ to itself. Rotations preserve angle measures, so $\angle CEA$ must be equal to $\angle CDB$ .
C
The $180^\circ$ rotation about $C$ maps point $B$ to point $A$ and point $D$ to point $E$ . Rotations preserve distances, so $\angle CEA$ must be equal to $\angle CDB$ .

Line & angle proofs