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Guggenheim Museum. Building big stuff can be expensive. So to work out details, artists and architects usually build scale models. Guggenheim Museum. A scale model is similar to the actually object that is to be built. And that does not mean that they are kind of alike. Guggenheim Museum. - PowerPoint PPT Presentation

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  • Guggenheim MuseumBuilding big stuff can be expensive. So to work out details, artists and architects usually build scale models.

  • Guggenheim MuseumA scale model is similar to the actually object that is to be built. And that does not mean that they are kind of alike.

  • Guggenheim MuseumA scale model is similar to the actually object that is to be built. And that does not mean that they are kind of alike.

  • SimilarityFigures that have the same shape but not necessarily the same size are similar figures. But what does same shape mean? Are the triangles similar?

  • SimilaritySimilar shapes can be thought of as enlargements or reductions with no irregular distortions.So two shapes are similar if one can be enlarged or reduced so that it is congruent to the original.

  • 6.3: Use Similar PolygonsObjectives:To define similar polygonsTo find missing measures in similar polygonsTo find the perimeter of similar polygons using a scale factor

  • Similar PolygonsTwo polygons are similar polygons if the corresponding angles are congruent and the corresponding sides are proportional.Similarity Statement:Corresponding Angles:Statement of Proportionality:

  • Example 1Use the definition of similar polygons to find the measure of x and y, assuming SMAL ~ BIGE.

  • 10Example 2When asked to find the length of segment DE given that the triangles are similar, Kenny says 10. Explain what is wrong with Kennys reasoning?

  • Example 3Determine whether or not the polygons below are similar.

  • Scale FactorIn similar polygons, the ratio of two corresponding sides is called a scale factor.What is the scale factor of the similar polygons shown?

  • Scale FactorExplain why the scale factor will always be the same for any two corresponding sides.

  • Example 4An artist painted a mural from the photograph shown at the right.If the artist used a scale of inch to represent 1 foot, what best represents the dimensions in feet of the mural?

  • Example 5A. , because corresponding angles of similar triangles are congruent.B. MK/MN = KJ/NL, because the ratios of the lengths of corresponding sides of similar triangles are equal.If , which of the following must be true?

  • Example 5C. KJ/LN = ML/MK, because the ratios of the lengths of corresponding sides of similar triangles are equal.D. , because corresponding angles of similar triangles are congruent.If , which of the following must be true?

  • Example 6In the diagrams shown, CORN~MAIZ. Recall that the scale factor of MAIZ to CORN is 3/2 or 1.5. Find the perimeter of each figure. What is the ratio of the perimeter of MAIZ to CORN?

  • Perimeter of Similar PolygonsIf two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.

  • Example 7In the diagram, ABCDE ~ FGHJK. Find the perimeter of ABCDE.

  • Example 8The polygons below are congruent. Are they also similar? If so, what is the scale factor?

  • Corresponding LengthsCorresponding Lengths in Similar PolygonsIf two polygons are similar, then the ratio of any two corresponding lengths in the polygons is equal to the scale factor of the similar polygons.

    SidesAltitudesMediansMidsegments

  • Example 9In the diagram TPR ~ XPZ. Find the length of the altitude PS.

  • AssignmentP. 367-9: 11, 13, 14, 22, 23P. 376-8: 1-3, 6, 8-13, 19, 20, 31, 32, 36, 39, 40-42Challenge Problems

    05 Similarity*

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