Question

222 test unit 2 parallel lines and angles show all work for full credit

1. fill in the blank. assume that all angles are right angles. 2 pts each

a. name a plane parallel to daeh.
b. name the segment parallel to (overline{bf}), (overline{cg}), and (overline{dh}).
c. name the segment perpendicular to (overline{ad}) and (overline{dc}).

Explanation:

Step1: Identify parallel planes

In a rectangular prism (the 3 - D shape in the problem), planes that do not intersect are parallel. Plane \(DAEH\) and plane \(CBFG\) are parallel.

Step2: Identify parallel segments

Segments that have the same direction and do not intersect are parallel. In a rectangular prism, \(\overline{AE}\) is parallel to \(\overline{BF}\), \(\overline{CG}\), and \(\overline{DH}\)

Step3: Identify perpendicular segments

In a rectangular prism, if a segment is perpendicular to two non - parallel segments in a plane, we look at the edges. \(\overline{DC}\) and \(\overline{AD}\) are in the plane \(ADCB\). The segment \(\overline{BC}\) (or \(\overline{AD}\) is in the plane \(ADCB\), and if we consider the 3 - D structure, \(\overline{AB}\) is perpendicular to both \(\overline{AD}\) and \(\overline{DC}\) (using the property of right - angled edges in a rectangular prism)

Answer:

a. \(CBFG\)
b. \(\overline{AE}\)
c. \(\overline{AB}\)