Lección 6
Semejanza
Exploremos figuras semejantes.
Problema 1
Cada diagrama tiene una pareja de figuras, una más grande que la otra. Para cada pareja, muestra que las dos figuras son semejantes identificando una secuencia de traslaciones, rotaciones, reflexiones y dilataciones que lleve la figura más pequeña a la más grande.
![Coordinate plane, x 0 to 4, y 0 to 6. Line through point A, the origin, C at 1 comma 2, E at 3 comma 6. Segments connect A, & C to point B at 1 comma 0. Segments connect E & C to point F at 3 comma 2.](https://staging-cms-im.s3.amazonaws.com/5wXB9BTeAqmgr9KTQ3aLsAFM?response-content-disposition=inline%3B%20filename%3D%228-8.2.B.PP.Image.03.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.B.PP.Image.03.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T143340Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b70b16357c0301ab70a04948fc201c1d1e802352cb07e483cc4b4cd948917c3b)
![Two triangles on a circular grid. Ask for further assistance.](https://staging-cms-im.s3.amazonaws.com/gDtbrvqDBWtUs4cQacqJkKm4?response-content-disposition=inline%3B%20filename%3D%228-8.2.B.PP.Image.04.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.B.PP.Image.04.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T143340Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=7406e0d97d89137b983238c9c12e6082fe3a4953ee2dafef4b554a3d7f37739b)
Problema 2
Estos son dos polígonos semejantes.
Mide las longitudes de los lados y los ángulos de cada polígono. ¿Qué observas?
![figure ABCD and figure EFGH on a grid.](https://staging-cms-im.s3.amazonaws.com/3EtfbbrKxN68Z5KAzaexR6Bh?response-content-disposition=inline%3B%20filename%3D%228-8.2.B.PP.Image.02.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.B.PP.Image.02.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T143340Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8d543f3ebfe71d2571b3237512a4cd83c9f32d8f99698541ec17aefd832b4d6d)
Problema 3
Cada figura muestra una pareja de triángulos semejantes, uno contenido en el otro. Para cada pareja, describe un punto y un factor de escala para usarlos en una dilatación que lleve el triángulo más grande al más pequeño. Utiliza una herramienta de medición para encontrar el factor de escala.
![Triangles A, B C, and A prime B C prime. A prime lies on side A, B. C prime lies on side B C.](https://staging-cms-im.s3.amazonaws.com/JS2VrKd4kvVqgTfqpttfjWYA?response-content-disposition=inline%3B%20filename%3D%228-8.2.B.PP.Image.05.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.B.PP.Image.05.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T143340Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=67ed07f1840e9a840d0a9182c7711cb6cb92270ce4704521731317ebf1b9554a)
![Triangles A, B C, and A, B prime C prime. B prime lies on side A, B. C prime lies on side A, C.](https://staging-cms-im.s3.amazonaws.com/tY3T5tQJZK3BdYysFQKBSMb4?response-content-disposition=inline%3B%20filename%3D%228-8.2.B.PP.Image.06.1.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.B.PP.Image.06.1.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T143340Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=08fa5f55a3d486e4ddb8e1faa5f7701d1761787287b292c64e8ce97491d1288a)