Eight beads are strung in a necklace with a clasp, how many ways can the beads be arranged?
1 answer:
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1. matches to E
<u>Corresponding parts:</u>
<em>Angles, sides, or vertices of two or more figures that are located in the same position when the figures are aligned.</em>
The term corresponding means that the parts of two or more figures match when turning, flipping or sliding them. In Figure 1, If we turn the object in green a certain angle, we will get to match both the sided and the angles of these two objects. Therefore, object in red and object in green are corresponding.
2. matches to B
<u>Angle:</u>
<em>If two corresponding angles of two or more triangles are congruent, then the triangles are similar</em>
From the Figure 2, for both triangles, the angles in red are corresponding and the angles in blue are corresponding as well. This does not mean that both triangles are the same (they might be), but they are similar, that is, the side lengths of these two triangles are proportional.
3. matches to C
<u>Similar:</u>
<em>has the same shape with proportional corresponding sides, but not necessarily the same size</em>
From the Figure 3, we can see that these two triangles are not the same, but the side lengths of these two triangles are proportional. This concept can be extended for any two or more objects.
4. matches to A
<u>Dilation:</u>
<em>transforms an object by making it larger or smaller</em>
To dilate an object means to enlarge or reduce the size of the object. The scale factor will determine how much larger or smaller the object will become. If this factor is greater than 1, the object will increase in size. Otherwise, if the factor is less than 1, the object will decrease in size. So, the dilated object will be similar to its original. On the other hand, when corresponding points of the original and dilated figures are connected by straight lines, the center of dilation is the point where all the lines meet. You can see this concept in Figure 4. There are two dilation here, the object in green has been reduced while the object in blue has been enlarged.
5. matches to D
<u>Scale model:</u>
<em>A representation or copy of an object that is proportionately larger or smaller than the actual size of the object</em>
In Figure 5, we have two object. A big object and a smaller one. So, we can say that the smaller one is an object to scale. In real life, we can see scale model. Think about the Eiffel Tower, there are objects that you can buy in a store that is a scale model of this tower. So, this is a representation of it.
