Similarity and Using Similar Triangles Similar Figures Similar
![Similarity and Using Similar Triangles Similarity and Using Similar Triangles](https://slidetodoc.com/presentation_image_h2/70c6d0f8c080cff7722703dd6b3e991a/image-1.jpg)
![Similar Figures �Similar figures have the same shape, but different size. �The angles and Similar Figures �Similar figures have the same shape, but different size. �The angles and](https://slidetodoc.com/presentation_image_h2/70c6d0f8c080cff7722703dd6b3e991a/image-2.jpg)
![Similar Polygons �To produce similar polygons, a dilation must have occurred (along with other Similar Polygons �To produce similar polygons, a dilation must have occurred (along with other](https://slidetodoc.com/presentation_image_h2/70c6d0f8c080cff7722703dd6b3e991a/image-3.jpg)
![Similar Polygons �To produce similar polygons, a dilation must have occurred �The side lengths Similar Polygons �To produce similar polygons, a dilation must have occurred �The side lengths](https://slidetodoc.com/presentation_image_h2/70c6d0f8c080cff7722703dd6b3e991a/image-4.jpg)
![Are the two figures similar? 9 cm �Measure parts of both figures. �How do Are the two figures similar? 9 cm �Measure parts of both figures. �How do](https://slidetodoc.com/presentation_image_h2/70c6d0f8c080cff7722703dd6b3e991a/image-5.jpg)
![What sequence of transformations changed the red figure into the brown figure? 9 cm What sequence of transformations changed the red figure into the brown figure? 9 cm](https://slidetodoc.com/presentation_image_h2/70c6d0f8c080cff7722703dd6b3e991a/image-6.jpg)
![Similar Triangles �Similar triangles have the same shape, but different size. �You can use Similar Triangles �Similar triangles have the same shape, but different size. �You can use](https://slidetodoc.com/presentation_image_h2/70c6d0f8c080cff7722703dd6b3e991a/image-7.jpg)
![�The two triangles in the diagram are similar. �To find the object’s height, you �The two triangles in the diagram are similar. �To find the object’s height, you](https://slidetodoc.com/presentation_image_h2/70c6d0f8c080cff7722703dd6b3e991a/image-8.jpg)
![What do you do next? �Once you have these three measurements, how do you What do you do next? �Once you have these three measurements, how do you](https://slidetodoc.com/presentation_image_h2/70c6d0f8c080cff7722703dd6b3e991a/image-9.jpg)
![Set up and solve the proportion �Height of object = Height of person Distance Set up and solve the proportion �Height of object = Height of person Distance](https://slidetodoc.com/presentation_image_h2/70c6d0f8c080cff7722703dd6b3e991a/image-10.jpg)
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![Similarity and Using Similar Triangles Similarity and Using Similar Triangles](https://slidetodoc.com/presentation_image_h2/70c6d0f8c080cff7722703dd6b3e991a/image-1.jpg)
Similarity and Using Similar Triangles
![Similar Figures Similar figures have the same shape but different size The angles and Similar Figures �Similar figures have the same shape, but different size. �The angles and](https://slidetodoc.com/presentation_image_h2/70c6d0f8c080cff7722703dd6b3e991a/image-2.jpg)
Similar Figures �Similar figures have the same shape, but different size. �The angles and side lengths will correspond just as they did in congruent figures, BUT… �The corresponding side lengths will not be congruent. They will be proportional �The corresponding angles will remain congruent
![Similar Polygons To produce similar polygons a dilation must have occurred along with other Similar Polygons �To produce similar polygons, a dilation must have occurred (along with other](https://slidetodoc.com/presentation_image_h2/70c6d0f8c080cff7722703dd6b3e991a/image-3.jpg)
Similar Polygons �To produce similar polygons, a dilation must have occurred (along with other possible transformations as well) �Write down which vertices in quadrilateral ABCD correspond to which PQRS. S R vertices in quadrilateral The arrow “→” means. Q“corresponds to. ” P �A → B→ �C → D→ S R �The corresponding angles REMAIN CONGRUENT!! � C � A P D B Q
![Similar Polygons To produce similar polygons a dilation must have occurred The side lengths Similar Polygons �To produce similar polygons, a dilation must have occurred �The side lengths](https://slidetodoc.com/presentation_image_h2/70c6d0f8c080cff7722703dd6b3e991a/image-4.jpg)
Similar Polygons �To produce similar polygons, a dilation must have occurred �The side lengths will be a new size, but they 3 will be proportional according to the scale factor. 4 2 �Write down the corresponding side lengths 5 RS �AB → PQ �CD→ SP BC → QR 9 DA → �The corresponding. Image side lengths side are=proportional the scale length set up a fraction factor RS 6 15 12 = 3 (the pre-image scaleside factor) 12 = AB 4 length PQ = 6 = 3 SP = 9 = 3 QR= 15= 3 ALL corresponding side lengths need to be 5 DA 3 BC CD 2 proportional
![Are the two figures similar 9 cm Measure parts of both figures How do Are the two figures similar? 9 cm �Measure parts of both figures. �How do](https://slidetodoc.com/presentation_image_h2/70c6d0f8c080cff7722703dd6b3e991a/image-5.jpg)
Are the two figures similar? 9 cm �Measure parts of both figures. �How do we use these numbers to determine if the figures are similar? �Find the scale factor. � 8 ÷ 24 = 1/3 � 3 ÷ 9 = 1/3 �Since the scale factor is the same for both sets of sides, the figures are similar. 24 cm 3 cm 8 cm
![What sequence of transformations changed the red figure into the brown figure 9 cm What sequence of transformations changed the red figure into the brown figure? 9 cm](https://slidetodoc.com/presentation_image_h2/70c6d0f8c080cff7722703dd6b3e991a/image-6.jpg)
What sequence of transformations changed the red figure into the brown figure? 9 cm �It could have been a 90˚ clockwise rotation followed by a dilation with a scale factor of 1/3. 24 cm �Is it possible that it could have been a dilation with a scale factor of 1/3 then a 90˚ clockwise rotation? 3 cm 8 cm
![Similar Triangles Similar triangles have the same shape but different size You can use Similar Triangles �Similar triangles have the same shape, but different size. �You can use](https://slidetodoc.com/presentation_image_h2/70c6d0f8c080cff7722703dd6b3e991a/image-7.jpg)
Similar Triangles �Similar triangles have the same shape, but different size. �You can use the relationships between corresponding parts of similar triangles to solve measurement problems.
![The two triangles in the diagram are similar To find the objects height you �The two triangles in the diagram are similar. �To find the object’s height, you](https://slidetodoc.com/presentation_image_h2/70c6d0f8c080cff7722703dd6b3e991a/image-8.jpg)
�The two triangles in the diagram are similar. �To find the object’s height, you need to measure three distances and use similar triangles. �What distances do you think we should measure? Object’s distance to mirror. Person ’s height Person’s distance to mirror.
![What do you do next Once you have these three measurements how do you What do you do next? �Once you have these three measurements, how do you](https://slidetodoc.com/presentation_image_h2/70c6d0f8c080cff7722703dd6b3e991a/image-9.jpg)
What do you do next? �Once you have these three measurements, how do you find the height of the traffic light? �Set up a proportion and solve for the missing height. 160 cm 600 cm 200 cm
![Set up and solve the proportion Height of object Height of person Distance Set up and solve the proportion �Height of object = Height of person Distance](https://slidetodoc.com/presentation_image_h2/70c6d0f8c080cff7722703dd6b3e991a/image-10.jpg)
Set up and solve the proportion �Height of object = Height of person Distance of object to mirror. 200 x = 600(160) � x = 160 200 x = 96, 000 x = 480 600 200 The height of the traffic light is 480 cm. 160 cm 600 cm 200 cm
Proving triangle similarity
Unit 2 lesson 3 proving triangles similar
Determine similar triangles angles
Congruent figures have the same
Proving figures are similar using transformations
Indirect measurement using similar triangles
Similarity in right triangles notes
Similar
Similarity in right triangles
8-1 similarity in right triangles answer key
8-1 similarity in right triangles