Question

given: ad || bc
prove: dc = 6 units
which step is missing?
a. △dca ≅ △bca by asa
b. △dac ≅ △bca by asa
c. △dca ≅ △bca by sas
d. △dac ≅ △bca by sas

Explanation:

Step1: Analyze the given information

We have \(AD\parallel BC\), so \(\angle DAC\cong\angle BCA\) (alternate - interior angles) and \(\angle DCA\cong\angle BAC\) (alternate - interior angles). Also, \(AC\cong AC\) (reflexive property).

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

The ASA congruence 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.
For \(\triangle DAC\) and \(\triangle BCA\), we have \(\angle DAC\cong\angle BCA\), \(AC = AC\) (included side), and \(\angle DCA\cong\angle BAC\).

Answer:

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