Geometry. Please help fast!!

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 ∠CDE? Be prepared to explain your choice for that angle. Use that measure to find all other angles involved.

On the discussion board 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

EXPLANATION THROUGH STEP BY STEP SOLUTION:

Treat AI as a single line acting as a transversal for the lines that need to be parallel.

Within each set of lines that need to be parallel, their acute angles must be congruent. For maximum stability, the acute angles between the two sets all must be congruent.

Both angles CDE and EDF need to be 180degrees minus twice the measure of the one of the congruent acute angles (any one given they are all the same measure). Cannot tell what the specific measure needs to be for maximum stability without knowing the proportional lengths of the segments.

Any pair of the acute angles previously referred to, within each of the two sets of parallel lines previously referred to, are corresponding, but NOT from one set to the other.

Given the transversals go through end points, there are NO alternate angles, interior or exterior, because alternate angles are on opposite sides of the transversal; and if the transversal is at the endpoints of the parallel lines, there are no angles at the transversal on the opposite side of angles of the parallel lines.