Question

geometry 4 - 4 day 1 hwk
name:
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.

1. label each pair of triangles congruent by sas, sss, aas, asa, or not enough information.

1.
ii.
iii.
iv.
2)
1.
ii.
iii.
iv.

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 \(AD\parallel BC\), \(\angle BCA = \angle DAC\) (alternate - interior angles).

Step2: Identify common side

\(AC = CA\) (reflexive property of equality).

Step3: Apply ASA congruence criterion

In \(\triangle ABC\) and \(\triangle CDA\), we have \(\angle BAC=\angle DCA\), \(AC = CA\), \(\angle BCA=\angle DAC\). By the Angle - Side - Angle (ASA) congruence criterion, \(\triangle ABC\cong\triangle CDA\).

Answer:

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