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://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=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T232858Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=631baa441d078434c65b257a9ef6990b5a300aa59af4433ed6c2a167afa9636c)
![Two triangles on a circular grid. Ask for further assistance.](https://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=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T232858Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=5fa3897951e2ce258002a51a6f7a137a63cf22c4600990a2c48285927647c3b2)
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://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=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T232858Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=5c43dc80fde711998472412ef651445802ae7d880f36689ddc11f6394ab97cdd)
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://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=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T232858Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=5900ea1d0af17d14d306d762230388ef67a4e33486763f650ccece1e2fa5ad1c)
![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://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=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T232858Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=6a4d400b45daec18017c39ae43a1cfab34cab7178a71cd91297922268568d493)