Question

1. quadrilateral abcd is a parallelogram. by definition, that means $overline{ab} parallel overline{dc}$ and $overline{bc} parallel overline{ad}$.

a. sketch parallelogram abcd, and then draw an auxiliary line $overline{ac}$ to show how abcd can be decomposed into 2 triangles.

Explanation:

1. First, sketch a four-sided figure where opposite sides are parallel: label the vertices in order as \(A\), \(B\), \(C\), \(D\) such that \(\overline{AB} \parallel \overline{DC}\) and \(\overline{BC} \parallel \overline{AD}\).
2. Then, draw a straight line connecting vertex \(A\) to vertex \(C\); this diagonal splits the parallelogram into two triangles, \(\triangle ABC\) and \(\triangle ADC\).

Answer:

1. Sketch of parallelogram \(ABCD\): A quadrilateral with \(\overline{AB}\) parallel to \(\overline{DC}\), and \(\overline{BC}\) parallel to \(\overline{AD}\), vertices labeled clockwise/counterclockwise in sequence.
2. Auxiliary line: Diagonal \(\overline{AC}\), which decomposes \(ABCD\) into \(\triangle ABC\) and \(\triangle ADC\).