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Question 172050: I am so sorry but I am having so much trouble understanding how to figure this out. I am being asked about union and intersections of line and rays and union and intersections of angles. I do not just want the answers I really wnat to understand how to do it. The textbook just does not make it clear to me. I have AD U BC there is a line w/two sided arrow over the AD and a line over BC. The second one BC U CF U FB with a line over all of them without any arrows. The third one is angle HCD intersects(symbol upsidedown U)angle ACF. And the fouth one is angle ICA intersects (symbol is the upsidedown U again) EG-this has a line with the two sided arrrows again.
The line ABCD has two other line crossing it (one at point B and the other at point C)and they intersect to create the top of a triangle above rays BC of line.
I pray this is not too complicated and you can help me anyway. I totally understand if you can't, and I have no money right now to offer any of you but when I do I will make a donation to you. I plan to keep your information so when I can I will contact you. I hope you do not feel like I am just saying this to get help. Honestly.
Again I am not just looking for the answers I need to understand how. Thank you so much in advance.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! I'm not sure how helpful I can be because I can't see the illustrations or diagrams that you are working with.
What I can do is define the symbols that you have used and discuss the implications somewhat.
Definition of a straight line. A connected set of infinitely many points. It extends infinitely far in two opposite directions. A line has infinite length, zero width, and zero height. Any two points on the line name it. A double-headed arrow over the letter designations of the two points indicates a line.
So, in your first example, AD is a line that passes through points A and D and extends infinitely far in either direction.
Definition of a ray: Just like a line, except that it has one end point and extends infinitely far in the other direction. The symbol above the letter designations of the two points would be a single headed arrow.
Definition of a line segment: Here we have a piece of a line with two end points. The symbol is a bar with no arrowheads.
So, again in your first example, BC is a line segment consisting of the points B and C and all of the infinitely many points between B and C, but not extending in either direction past B or C.
Remember that all of these definitions are ways of describing sets of points. Here is where we are able to apply the ideas of Union and Intersection. Remember from your study of sets: The union of two sets is a set that includes all of the elements that are in either set or both. The intersection of two sets includes those elements that occur in both sets.
Examples:
Consider the sets S1: {A, B, C} and S2: {A, D, E}
The union of S1 and S2 (S1 U S2) would be {A, B, C, D, E}
The intersection of S1 and S2 (denoted with an upside-down U) would be {A} because the element 'A' is the only element both sets have in common.
In the case of your first example, I have to assume that one of the endpoints of BC acually lies on the line AD and the other endpoint does not. Given that, the union of line AD and line segment BC describes a pair of supplementary angles, namely angle ABC and angle DBC. On the other hand, if all four points mentioned, namely A, B, C, and D are colinear (that is, they all lie on the same line) then the union of the two lines (more correctly the union of these two sets of points) is simply the line AD because ALL of the elements of segment BC would be already contained in AD.
I hope this at least gets you started.
John
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