Question

In construction, the precision used to build a structure directly influences the strength of the structure. In the Rocky Mountains, many houses’ roofs are built using trusses, which are strong enough to support the heavy load from snow, but light enough to build in a stockyard and transport to the construction site. Chris works in the stockyard. He has been told he needs to build a series of trusses for a new house using the pattern below. He has also been told the pattern may be inaccurate—so he needs to check and make sure the following features are all parallel, and adjust the pattern before starting. Describe the angles you would need to know to verify that BC, DE and FG are all parallel to each other, and CD, EF and GH are also parallel. What could be an appropriate measure for angle CDE ? Be prepared to explain your choice for that angle. Use that measure to find all other angles involved. Answer the following:

1.What method(s) can Chris use to make sure the segments in the pattern are all parallel and that his new trusses are built precisely and strongly?
2.What method(s) can Chris’s boss use to verify the precision of the trusses Chris builds?
3.If you lived in a mountainous area with a lot of snow, how much leeway would you feel comfortable giving your home’s builders as they design and build your trusses? Why?
4.Identify any alternate interior angles, corresponding angles, and/or alternate exterior angles.

Answer 1

To verify the parallelism of the trusses, Chris needs to check the congruence of corresponding angles. The measure of angle CDE can help in assessing the parallelism. Chris can measure the angles using a protractor or a measuring tool.

Step-by-step explanation:

To verify that BC, DE, and FG are all parallel to each other, Chris would need to check if the corresponding angles are congruent. He can do this by measuring the angles using a protractor or a measuring tool and comparing them. If the corresponding angles are equal, then BC, DE, and FG are parallel.

Similarly, to verify that CD, EF, and GH are parallel, Chris can measure the corresponding angles and check for congruence. If the corresponding angles are equal, then CD, EF, and GH are parallel.

An appropriate measure for angle CDE would be the angle formed by the intersection of line segments CD and DE. Chris can use a protractor or a measuring tool to measure angle CDE, which would help him ascertain the parallelism of the trusses.