7 3 Similar Triangles Objectives Identify similar triangles
![7. 3 Similar Triangles 7. 3 Similar Triangles](https://slidetodoc.com/presentation_image_h2/27f37696ca81d0c28892fec5bc941287/image-1.jpg)
7. 3 Similar Triangles
![Objectives § Identify similar triangles § Use similar triangles to solve problems Objectives § Identify similar triangles § Use similar triangles to solve problems](http://slidetodoc.com/presentation_image_h2/27f37696ca81d0c28892fec5bc941287/image-2.jpg)
Objectives § Identify similar triangles § Use similar triangles to solve problems
![Similar Triangles § Previously, we learned how to determine if two triangles were congruent Similar Triangles § Previously, we learned how to determine if two triangles were congruent](http://slidetodoc.com/presentation_image_h2/27f37696ca81d0c28892fec5bc941287/image-3.jpg)
Similar Triangles § Previously, we learned how to determine if two triangles were congruent (SSS, SAS, ASA, AAS). There also several tests to prove triangles are similar. § Postulate 6. 1 – AA Similarity 2 s of a Δ are to 2 s of another Δ § Theorem 6. 1 – SSS Similarity corresponding sides of 2 Δs are proportional § Theorem 6. 2 – SAS Similarity corresponding sides of 2 Δs are proportional and the included s are
![Example 1: In the figure, and Determine which triangles in the figure are similar. Example 1: In the figure, and Determine which triangles in the figure are similar.](http://slidetodoc.com/presentation_image_h2/27f37696ca81d0c28892fec5bc941287/image-4.jpg)
Example 1: In the figure, and Determine which triangles in the figure are similar.
![Example 1: by the Alternate Interior Angles Theorem. Vertical angles are congruent, Answer: Therefore, Example 1: by the Alternate Interior Angles Theorem. Vertical angles are congruent, Answer: Therefore,](http://slidetodoc.com/presentation_image_h2/27f37696ca81d0c28892fec5bc941287/image-5.jpg)
Example 1: by the Alternate Interior Angles Theorem. Vertical angles are congruent, Answer: Therefore, by the AA Similarity Theorem,
![Your Turn: In the figure, OW = 7, BW = 9, WT = 17. Your Turn: In the figure, OW = 7, BW = 9, WT = 17.](http://slidetodoc.com/presentation_image_h2/27f37696ca81d0c28892fec5bc941287/image-6.jpg)
Your Turn: In the figure, OW = 7, BW = 9, WT = 17. 5, and WI = 22. 5. Determine which triangles in the figure are similar and why. I Answer:
![Example 2: ALGEBRA Given QT 2 x 10, UT 10, find RQ and QT. Example 2: ALGEBRA Given QT 2 x 10, UT 10, find RQ and QT.](http://slidetodoc.com/presentation_image_h2/27f37696ca81d0c28892fec5bc941287/image-7.jpg)
Example 2: ALGEBRA Given QT 2 x 10, UT 10, find RQ and QT.
![Example 2: Since because they are alternate interior angles. By AA Similarity, Using the Example 2: Since because they are alternate interior angles. By AA Similarity, Using the](http://slidetodoc.com/presentation_image_h2/27f37696ca81d0c28892fec5bc941287/image-8.jpg)
Example 2: Since because they are alternate interior angles. By AA Similarity, Using the definition of similar polygons, Substitution Cross products
![Example 2: Distributive Property Subtract 8 x and 30 from each side. Divide each Example 2: Distributive Property Subtract 8 x and 30 from each side. Divide each](http://slidetodoc.com/presentation_image_h2/27f37696ca81d0c28892fec5bc941287/image-9.jpg)
Example 2: Distributive Property Subtract 8 x and 30 from each side. Divide each side by 2. Now find RQ and QT. Answer:
![Your Turn: ALGEBRA Given and CE x + 2, find AC and CE. Answer: Your Turn: ALGEBRA Given and CE x + 2, find AC and CE. Answer:](http://slidetodoc.com/presentation_image_h2/27f37696ca81d0c28892fec5bc941287/image-10.jpg)
Your Turn: ALGEBRA Given and CE x + 2, find AC and CE. Answer:
![Example 3: INDIRECT MEASUREMENT Josh wanted to measure the height of the Sears Tower Example 3: INDIRECT MEASUREMENT Josh wanted to measure the height of the Sears Tower](http://slidetodoc.com/presentation_image_h2/27f37696ca81d0c28892fec5bc941287/image-11.jpg)
Example 3: INDIRECT MEASUREMENT Josh wanted to measure the height of the Sears Tower in Chicago. He used a 12 -foot light pole and measured its shadow at 1 P. M. The length of the shadow was 2 feet. Then he measured the length of the Sears Tower’s shadow and it was 242 feet at that time. What is the height of the Sears Tower?
![Example 3: Assuming that the sun’s rays form similar triangles, the following proportion can Example 3: Assuming that the sun’s rays form similar triangles, the following proportion can](http://slidetodoc.com/presentation_image_h2/27f37696ca81d0c28892fec5bc941287/image-12.jpg)
Example 3: Assuming that the sun’s rays form similar triangles, the following proportion can be written. Now substitute the known values and let x be the height of the Sears Tower. Substitution Cross products
![Example 3: Simplify. Divide each side by 2. Answer: The Sears Tower is 1452 Example 3: Simplify. Divide each side by 2. Answer: The Sears Tower is 1452](http://slidetodoc.com/presentation_image_h2/27f37696ca81d0c28892fec5bc941287/image-13.jpg)
Example 3: Simplify. Divide each side by 2. Answer: The Sears Tower is 1452 feet tall.
![Assignment § Geometry Pg. 302 # 10 – 20, 24, 25, 26, 28 § Assignment § Geometry Pg. 302 # 10 – 20, 24, 25, 26, 28 §](http://slidetodoc.com/presentation_image_h2/27f37696ca81d0c28892fec5bc941287/image-14.jpg)
Assignment § Geometry Pg. 302 # 10 – 20, 24, 25, 26, 28 § Pre-AP Geometry Pg. 302 #10 – 28, 30, 32
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