In 1603, German astronomer Christoph Scheiner began to copy and scale diagrams using an instrument that came to be known as the pantograph. By moving a pencil attached to a linkage, Scheiner was able to produce a second image that was enlarged. Do some brief research on Scheiner’s invention. Describe how the pantograph works and how it is able to produce an enlarged image. How does the operation of the pantograph relate to dilations and similarity? How can you use similar triangles to describe why the pantograph works as it does? Write an abbreviated paragraph proof using similar triangles to explain the design. In many instances, the pantograph has been replaced by other means for enlarging images. What has the pantograph been replaced by? Explain.

1. The writing utensil’s placement facilitates the drawing of two or more lines with a single stroke of the pantograph. This means while drawing an image two or more copies of varying sizes may be created at the same time. The pantograph mirror is used to extend or retract an image.

2. The operation of a pantograph relates to dilations and similarity in that both of the processes are done on the graph and it is possible to use similar triangles through measuring the size of the triangles. Pantograph contains links that maybe arranged in other ways because they contain a parallelogram.

3. You can use similar triangles to describe the working of the pantograph because the ratio of similitude is set when determining where to put the pin. When one triangle is moved with the part being specific to the point (tracing style), along the outline of the image, an enlarged/reduced version of the image is created by movement of the other triangle (drawing stylus point).

4. Pantograph has been replaced by modern ways of producing duplicates such as photocopying, mass printing and digital filing. This is because the technique is currently outdated and the fact that it is difficult to use then now due to their complex designs which does not allow users to properly grip an actual writing utensil like the pen.

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1.    The pin’s placement helps to make two drawings simultaneously. This is that while drawing an image a copy, which may vary in size, is created at the same time.

2.    The pantograph relates to dilations and similarity due to the use of similar triangles that affect the scale of the second drawing.  

3.    The use of similar triangles illustrates the process of the pantograph because the ratio of similitude is set when determining where to place the pin. When a triangle is moved while tracing a line, along with the outline of the image, an enlarged/reduced version of the image is created by the other pantograph's end.

4.    The pantograph is now obsolete and has been replaced by several different ways of producing duplicates such as photocopying, mass printing, and digital filing.

d. it is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

step-by-step explanation:

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc