# 8.8 similarity and dilations 1

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• 1.Lesson8.7 , For use with pages439-444 Tell whether the figure is a reflection in the line shown? 1. 2.

2. Lesson8.7 , For use with pages439-444 Tell whether the figure is a reflection in the line shown? ANSWER no 1. ANSWER yes 2. 3. 8.8 Similarity and Dilations 4. Essential Questions

• What are the similarities and differences among transformations?
• How are the principles of transformational geometry used in art, architecture and fashion?
• What are the applications for transformations?

5. Similar Polygons

• Similar polygonshave the same shape but can be different sizes. The symbol~ means is similar to.

6. 7. EXAMPLE1 Identifying Similar Polygons STEP 1 Decide whether corresponding angles are congruent. Each angle measures90 . Tell whether the television screens are similar. A E B F C G D H 8. STEP 2 Decide whether corresponding side lengths are proportional. EXAMPLE1 Identifying Similar Polygons 30inches 18 inches 40inches 24 inches = ? 5 3 = 5 3 ANSWER Yes, quadrilateralABCD~quadrilateralEFGH . 9. SOLUTION EXAMPLE2 Standardized Test Practice Corresponding side lengths are proportional. Write a proportion. Substitute given values. Solve the proportion. KL NP = LM PQ KL 12 M = 10M 5 M KL = 24 10. EXAMPLE3 Using Indirect Measurement Height Alma is5feet tall and casts a7foot shadow. At the same time, a tree casts a14foot shadow. The triangles formed are similar. Find the height of the tree. 11. SOLUTION EXAMPLE3 Using Indirect Measurement You can use a proportion to find the height of the tree. Write a proportion. Substitute given values. Solve the proportion. Trees height Almas height = Length of trees shadow Length of Almas shadow xfeet 5 feet = 14feet 7 feet x10 = ANSWER The tree is10feet tall. 12. Dilation

• Stretches or shrinks a figure
• The image created by a dilation is similar to the original figure.
• Scale factor : of a dilation is the ratio of a side length after the dilation to the corresponding side length before the dilation.

13. 14. Dilations

• National Library of Virtual Manipulatives
• Geometry 6-8
• Transformations-Dilations

15. 16.

• Dimensions can be scaled UP or scaled DOWN as stated before.
• To scale up, means you would multiply by a number that is _______________.
• To scale down, you would multiply by a number that is _________________

greater than one. less than one 17. EXAMPLE4 Dilating a Polygon QuadrilateralABCDhas verticesA ( 1, 1),B (0, 1), C(2, 2),andD (3, 0).Dilate using a scale factor of3 . SOLUTION Original Image (x, y) A (1, 1 ) B ( 0, 1 ) C ( 2, 2 ) D ( 3, 0 ) ( 3 x ,3 y ) A ( 3, 3 ) B ( 0, 3 ) C ( 6, 6 ) D ( 9, 0 ) 18. EXAMPLE4 Dilating a Polygon QuadrilateralABCDhas verticesA ( 1, 1),B (0, 1), C(2, 2),andD (3, 0).Dilate using a scale factor of3 . SOLUTION Graph the quadrilateral. Find the coordinates of the vertices of the image. Graph the image of the quadrilateral. Original Image (x, y) A (1, 1 ) B ( 0, 1 ) C ( 2, 2 ) D ( 3, 0 ) ( 3 x ,3 y ) A ( 3, 3 ) B ( 0, 3 ) C ( 6, 6 ) D ( 9, 0 ) 19.

• Graph the polygon with verticesV (0, 0) ,W (4, 6) , andX (4, 2) . Dilate by the scale factor, and graph the image.

• Page 450 #1-8, 12, 14
• Number 12: D (2,6)
• Number 14: k =2

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