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

Guggenheim Museum similar 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 similar 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.

Similarity similar figures Figures that have the same shape but not necessarily the same size are similar figures. But what does “same shape mean”? Are the triangles similar? NOT Similar

Similarity enlargements reductions Similar 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 Polygons Objectives: 1.To define similar polygons 2.To find missing measures in similar polygons 3.To find the perimeter of similar polygons using a scale factor

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

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

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

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

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

Scale Factor Explain why the scale factor will always be the same for any two corresponding sides.

Example 4 An artist painted a mural from the photograph shown at the right. If the artist used a scale of ½ inch to represent 1 foot, what best represents the dimensions in feet of the mural?

Example 5 A., 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 5 C. 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 6 In 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 Polygons If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.

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

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

Corresponding Lengths Corresponding Lengths in Similar Polygons If 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. SidesAltitudes MediansMidsegments

Example 9 In the diagram ΔTPR ~ ΔXPZ. Find the length of the altitude PS.

Assignment P : 11, 13, 14, 22, 23 P : 1-3, 6, 8- 13, 19, 20, 31, 32, 36, 39, Challenge Problems