Note: 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.
Without the diagram, it is difficult to provide a definitive answer. However, based on the given information, it is possible for the side pieces of the frame to be parallel. If the top section of the window frame is cut with a 37º angle on each end, and the side pieces each have a 50º angle cut at their top ends, it suggests that the angles on the top and bottom sections of the side pieces are equal. If the opposite sides of the frame have equal angles, then the side pieces would be parallel. However, it is important to view the diagram to confirm this.
To determine if the side pieces of the window frame will be parallel, we need to analyze the angles.
Given that the top section of the window frame has a 37º angle cut on each end, and the side pieces have a 50º angle cut at their top ends, we can compare these angles.
If the side pieces were parallel, each pair of corresponding angles would be equal.
Looking at the given information, we can see that the angle on the top section is smaller (37º) than the angle on the side pieces (50º).
Therefore, the side pieces of the frame will not be parallel since the angles on each end differ in size.
To determine whether the side pieces of the frame will be parallel, we need to understand the properties of angles.
In a quadrilateral, the sum of all interior angles is equal to 360 degrees. If the opposite angles are equal, then the sides will be parallel.
Looking at the given information, we can see that the top section of the window frame has a 37-degree angle on each end. Let's call the bottom angle of this section Angle A.
Next, we are told that the side pieces each have a 50-degree angle cut at their top ends. Let's call the bottom angle of each side piece Angle B.
Now, consider the quadrilateral formed by the top section and one side piece. According to the information, we have four angles: Angle A, Angle B, and two right angles (90 degrees each) at the bottom.
Using the fact that the sum of interior angles in a quadrilateral is 360 degrees, we can write the equation: Angle A + Angle B + 90 + 90 = 360.
Simplifying the equation, we have: Angle A + Angle B = 180.
We can see that the sum of Angle A and Angle B is equal to 180 degrees. This tells us that Angle A and Angle B are supplementary angles.
So, if Angle A is 37 degrees, Angle B must be 180 - 37 = 143 degrees.
Since Angle B is 143 degrees, we can conclude that the side pieces of the frame will not be parallel. This is because the opposite angles (Angle B) of the quadrilateral formed by the top section and one side piece are not equal.