Question

show all of your work on this worksheet and then enter your answers on formative. both are required in order to receive credit for the assignment.
label each pair of triangles congruent by sas, sss, aas, asa, or not enough information.
1)
2)

1. given: ( overline{ab}paralleloverline{dc},overline{ad}paralleloverline{bc} )

prove: ( \triangle abccong\triangle cda )

Explanation:

Step1: Use parallel line properties

Since \(AB\parallel DC\), \(\angle BAC=\angle DCA\) (alternate - interior angles). Since \(AD\parallel BC\), \(\angle DAC = \angle BCA\) (alternate - interior angles). Also, \(AC = CA\) (common side).

Step2: Apply ASA (Angle - Side - Angle) congruence criterion

In \(\triangle ABC\) and \(\triangle CDA\), we have \(\angle BAC=\angle DCA\), \(AC = CA\), \(\angle BCA=\angle DAC\). By the ASA (Angle - Side - Angle) congruence rule, if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.

Answer:

\(\triangle ABC\cong\triangle CDA\) by ASA.