Question

statements reasons
\\( \overline { a d } \parallel \overline { b c } \\) given
\\( \angle d a c \cong \angle b c a \\) alternate interior angles theorem
\\( \overline { a c } \cong \overline { a c } \\) reflexive property of congruence
\\( \angle d c a \cong \angle b a c \\) alternate interior angles theorem
? ?
\\( \overline { d c } \cong \overline { b a } \\) cpctc
\\( d c = b a \\) definition of congruent sides
\\( d c = 6 \\) units substitution property of equality
which step is missing?
o a. \\( \triangle d c a \cong \triangle b c a \\) by sas
o b. \\( \triangle d a c \cong \triangle b c a \\) by asa
o c. \\( \triangle d c a \cong \triangle b c a \\) by asa
o d. \\( \triangle d a c \cong \triangle b c a \\) by sas

Explanation:

Step1: Analyze the given congruent parts

We have \(\angle DAC\cong\angle BCA\), \(\overline{AC}\cong\overline{AC}\), and \(\angle DCA\cong\angle BAC\).

Step2: Recall the ASA (Angle - Side - Angle) congruence criterion

The ASA criterion states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
In \(\triangle DAC\) and \(\triangle BCA\), \(\angle DAC\) and \(\angle BCA\) are angles, \(\overline{AC}\) is the included side, and \(\angle DCA\) and \(\angle BAC\) are the other angles.

Answer:

B. \(\triangle DAC\cong\triangle BCA\) by ASA