Question

use the reason bank to complete the two - column proof. (see example 1.)

1. use the statements bank to complete the two - column proof.

given: \\( \overline { a b } \cong \overline { c d } \\), \\( \overline { a b } \parallel \overline { c d } \\)
prove: \\( \triangle a b c \cong \triangle c d a \\)

statements bank \\( \triangle a b c \cong \triangle c d a \\) \\( \overline { a c } \cong \overline { a c } \\) \\( \angle 1 \cong \angle 2 \\) \\( \overline { a b } \cong \overline { c d } \\)

Explanation:

Step1: Write the first given statement

\(\overline{AB}\cong\overline{CD}\)

Step2: Use the parallel lines to get angle congruence

Since \(\overline{AB}\parallel\overline{CD}\), by the Alternate Interior Angles Theorem, \(\angle1\cong\angle2\)

Step3: Use the reflexive property

\(\overline{AC}\cong\overline{AC}\)

Step4: Apply the SAS Congruence Theorem

\(\triangle ABC\cong\triangle CDA\)

Answer:

1. \(\overline{AB}\cong\overline{CD}\)
2. \(\angle1\cong\angle2\)
3. \(\overline{AC}\cong\overline{AC}\)
4. \(\triangle ABC\cong\triangle CDA\)