Using Similar Triangles Butterflies Pinwheels and Wallpaper 4

Using Similar Triangles Butterflies, Pinwheels and Wallpaper 4. 4

Learning Goal 1 (8. G. A. 3 & 4): The student will understand use informal arguments to prove congruency and similarity using physical models, transparencies or geometry software. 4 In addition to level 3. 0 and above and beyond what was taught in class, I may: Make connection with real-world situations Make connection with other concepts in math Make connection with other content areas. 3 I understand use informal arguments to prove congruency and similarity using physical models, transparencies or geometry software. informally prove similarity of triangles Use scale factors to create and analyze dilations. 2 1 I understand With help congruency and from the similarity using teacher, I physical have models, partial transparencies success or geometry with the software. unit content. construct triangles Calculate dilations with scale factors. 0 Even with help, I have no success with the unit content.

Similar Triangles �Similar triangles have the same shape, but are usually a different size. �You can use the relationships between corresponding parts of similar triangles to solve measurement problems.

Similar Triangles �The diagram shows a method for calculating the height of an object that is difficult to measure directly. �Place a mirror on a leveled spot at a convenient distance from the object. �Back up from the mirror until you see the reflection of the top of the object in the center of the mirror.

�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 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 of object to mirror Distance of person 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

Labsheet 4. 4