Your teacher will grade your responses to questions 4–8 to ensure you receive proper credit for your answers.
A carpenter cut the top section of a window frame with a 37º angle on each end. The side pieces each have a 50º angle cut at their top ends, as shown. Will the side pieces of the frame be parallel? Explain. Diagram not to scale.
An image of three quadrilaterals is shown.· The top image is a trapezoid with its shorter base on the bottom.
· The angles formed by the longer base and the legs are both labeled 37 degree-sign.
· The left side image is a trapezoid with its shorter base on the right and its diagonal leg on the top.
· The angle formed by the longer base and the diagonal leg is labeled 50 degree-sign.
· The right side image is a trapezoid congruent to the one on the left with its shorter base on the left and its diagonal leg on the top.
· The angle formed by the longer base and the diagonal leg is labeled 50 degree-sign.
(2 points)
No, the side pieces of the frame will not be parallel. This can be seen from the diagram where the angles of the top section and the side sections are different. In the top section, each end has a 37º angle, while in the side sections, each end has a 50º angle. Since the angles are different, the side pieces will not be parallel.
To determine if the side pieces of the window frame will be parallel, we need to analyze the angles in the diagram.
In the top image of the trapezoid, we have a 37º angle formed by the longer base and the legs. The left side image also has a 37º angle formed by the longer base and the diagonal leg, while the right side image has a 50º angle formed by the longer base and the diagonal leg.
If we compare the angle measurements in the left and right side images, we see that they are not equal. Therefore, the side pieces of the frame will not be parallel.