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Refer to the polygon below.a. How many vertices does it have? List them.b. How many sides does it have? List them.c. How many diagonals does it have? List them.d. Tell which of the following are acceptable ways of naming the polygon.quadrilateral $A B C D$quadrilateral $C D B A$quadrilateral $A C B D$quadrilateral $B A D C$CAN'T COPY THE GRAPH

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a. four; $A, B, C, D$b. four; $\overline{A B}, \overline{B C}, \overline{C D}, \overline{D A}$c. two; $\overline{A C}, \overline{B D}$d. yes, no, no, yes

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Chapter 9

An Introduction to Geometry

Section 6

Quadrilaterals and Other Polygons

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e. All right, so for hurt a we're looking specifically at the Vergis is remember, the vergis is air like the coroner, sort of. So we see four Vergis is here on this shape because it is a quadrilateral. So four vergis ease on. We label the vergis is by their letters. So we have Vergis is a be c and D on this ship for part B. We're talking about the sides again. The shape has four sides because it's a quadrilateral again, using the letters, we have side length a B, and it's easiest to name easier if you go around the shape so silent that is indicated by this line above the letters A B, then we have side length BC. So you're using the vergis? Is that connect the length side C. D and then side d A. You also could write these in the opposite order so I could have silent be a These two side lengths here would be talking about this same side. Either one's fine. All right. For diagonals, remember, diagonals go through the shape. So for diagonals, we have part C. We have two diagonals forming this sort of X pattern through the shape. So with a rough sketch here we have a shape that looks something like this. Mm. Sort of like that. Um and so are diagonals. Are the lines going from constant non consecutive virtus ease? So these will be our two diagonals. So using those letters to name them, we have Dagnall A, C and Dagnall be de finally in part D. We want to tell which of the ways are okay for naming this shape. So the key thing about the name in the shape is you have to go around the shape so you want to name the Vergis is in order that they appear around the shape so a B C D is correct. Those are the order that we see them appear in C. D. B. A is incorrect because DB is a diagonal. So nix that one A C B. D is also incorrect because remember, a C is a diagonal. So next that one our last one b a. D. C is correct. So these are the two ways that you could need in this quadrilateral. And there are all of your solutions. We have four. Vergis is four sides to diagonals and two ways of naming this quadrilateral

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