EQ: How do we know if polygons are similar?

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Presentation transcript:

EQ: How do we know if polygons are similar? Similar Polygons EQ: How do we know if polygons are similar? We will discuss and write properties of similar polygons in our summaries and in practice problems.

What are similar polygons? In order for two figures to be similar, you can show that all sides are proportional and all corresponding angles are congruent. --OR— there is a combination of transformations and a dilation that carry one figure onto the other. What are properties of similar polygons? We will discuss and write properties of similar polygons in our summaries and in practice problems.

What are properties of similar polygons? Example: Two quadrilaterals are shown below. Are these quadrilaterals similar? Explain why or why not. What are properties of similar polygons? We will discuss and write properties of similar polygons in our summaries and in practice problems.

What are properties of similar polygons? Example: Two farmers each have triangular plots of land. A model of their land is shown in the diagram below with approximate values shown for the lengths. Part A: Are the plots of land similar? Why or why not? Part B: What is the approximate value of x? What are properties of similar polygons? We will discuss and write properties of similar polygons in our summaries and in practice problems.

What are properties of similar polygons? Part A: Is there a sequence of rigid motions and dilations that takes Figure 1 onto Figure 2? Explain your reasoning. Part B: Based on your answer to Part A, are the two figures similar? Explain your reasoning. What are properties of similar polygons? We will discuss and write properties of similar polygons in our summaries and in practice problems.

What are properties of similar polygons? Example: Which of the following pairs of figures MUST be similar? (select all that apply) What are properties of similar polygons? We will discuss and write properties of similar polygons in our summaries and in practice problems.

Three rectangles are drawn on the coordinate plane to the right. Part A: Which of the following statements correctly explains whether or not Rectangles 1 and 2 are similar? A. Rectangles 1 and 2 are similar since all rectangles are similar. B. Rectangles 1 and 2 are not similar since the two rectangles have different sizes. C. Rectangles 1 and 2 are not similar since the two rectangles have different orientations. D. Rectangles 1 and 2 are similar since a set of rigid motions and dilations carries one to the other. What are properties of similar polygons? We will discuss and write properties of similar polygons in our summaries and in practice problems.

Three rectangles are drawn on the coordinate plane to the right. Part B: Select each statement that is true about Rectangles 1 and 3. A. Rectangle 1 and Rectangle 3 are similar. B. Rectangle 1 and Rectangle 3 are not similar. C. A rotation followed by dilation of 2 carries Rectangle 1 onto Rectangle 3. D. A rotation followed by dilation of ½ carries Rectangle 1 onto Rectangle 3. What are properties of similar polygons? We will discuss and write properties of similar polygons in our summaries and in practice problems.

Now you try: Try #1-4 from the Similar Polygons worksheet. Compare your answers with a partner. Discuss the essential question. Were you able to answer it correctly? Complete the rest of the worksheet.