*n 56% A student.desmos.com 3 Lesson 15: Finding All the Unknown Values in Tria... Salem 14 of 15 Next > 6) Multi-Select and Short Answer. Worth 4 points. 6. Tyler was trying to prove that all rhombuses are similar. He thought, "If I draw 2 rhombuses, I can find dilations that will take one rhombus exactly onto the other." Then he wrote a proof. All rhombuses are not similar. Which steps in Tyler's proof have flaws? Explain what is wrong with each step that is wrong. (Select all that apply.) O Step 1: Let ABCD and WXYZ be rhombuses. By the definition of a rhombus, AB = BC = CD = DA and WX XY = YZ = ZW. O Step 2: Dilate rhombus ABCD by the scale factor given by WX Side A'B' will be the same length as WX because of AB how I chose the scale factor. Because all sides of a rhombus are congruent, B'C' will be the same length as WX and therefore the same length as XY, C'D'will be the same length as YZ, and A'D' will be the same length as WZ. That means all the corresponding sides of A'B'C'D' and WXYZ will be the same length. O Step 3: If all the sides in 2 figures are proportional, then those 2 figures are similar, so there must be a sequence of transformations that take ABCD onto WXYZ using dilations and rigid motions. Step 4: Translate A'B'C'D' by the directed line segment A'W so that A" and W coincide. O Step 5: Rotate A"B"C"D" by angle B"WX so that B"" and X coincide. Now segments A"B"' and WX coincide. O Step 6: If needed, reflect A"''B'C"'D"' over segment WX so that D" and Z are on the same side of WX. Now segments A"'D" and WZ coincide. O Step 7: Once 3 vertices of the rhombus are lined up, the other vertex has to line up as well or else the shapes wouldn't be rhombuses. So, we have shown we can use rigid motions and dilations to line up any 2 rhombuses, and therefore, all rhombuses are similar.
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
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