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Use the information below to answer questions 1-4. The properties of lines and angles are used all the time in creative fields. In fashion design, for example, the makers of clothing patterns use parallel and perpendicular guidelines (among other lines and angles) to make sure that their clothing patterns don’t slant unpredictably. You can see this on the example pattern below, which shows half of the front of a shirt (with no sleeve or collar). Line AB is the center front. The triangular outlines are darts, or areas of fabric that are going to be sewn shut to create more shape in the clothing. The grid on the pattern paper represents a coordinate plane with each box being 1 unit.
Questions 1-3 can each be answered with one word; the answer to question 4 is a number. (Note: the x-coordinates of the endpoints of line segment AB are equal. So are the x coordinates of the endpoints of CD as well as FJ.)
Line segments AB, CD, and FJ are:
Line segments CD and GI are:
Line segment EF ______ angle GFH.
Line segment EF has endpoints at (2, 12) and (6.7, 13) on your pattern paper. How many units long is EF, rounded to the nearest tenth?
Use the information below to answer questions 5 and 6. Architects use all of the line and angle properties that appear on the ACT in their designs. For example, they use same-side interior angles to make sure that beams are parallel. More great examples of how architects use lines and angles can be found here.
You are constructing a building that includes the room in the plan below. If angle A is 75 degrees, what must angle B equal to ensure that walls 1 and 2 of the room are parallel?
What type of angle is angle B? (Answer is one word)
Use the information below to answer questions 7-9. Lines and angles are also used in perspective drawing, with objects positioned along lines that are drawn from one or more “vanishing points” on the horizon. For a good explanation of what this means and an introduction to how to draw in basic 1, 2, and 3-point perspective, watch this 10-minute tutorial.
You are practicing your drawing skills and would like to recreate the photo below in 1-point perspective.
You draw your vanishing point, then make guide lines using a ruler so that you know where to place your buildings. The two vertical lines (in purple) that you draw to mark the sides of the buildings are parallel.
7. If angle A is 95 degrees, what is the measure of angle B?
What is the measure of angle C?
What is the measure of angle D?
Master Question: Use the following information to answer question 10. Two equal masses always scatter at a right angle to each other after colliding. Let’s take the game of pool as an example. Imagine you have a ball right on the edge of one of the side pockets, and you can choose to place your cue ball at one of the 5 locations shown in the diagram. You want to knock the shaded ball directly into the side pocket so that it has no chance to ricochet (bounce) out. The following rule tells you how best to do this;
“Two objects of equal mass scatter at right angles to one another after a non-head-on collision.”
Consider the pool table drawn below. The six pockets are labeled “U” through “Z”. 5 cue-ball positions and respective trajectories are represented by rays 1 through 5. Assuming the underlined statement above is true, which position/shot (1 through 5) best guarantees that the shaded ball will be hit directly into pocket Y? For the purpose of this problem, treat the cue ball as a point (it has a negligible radius).