Lesson 6
Similarity
Problem 1
Each diagram has a pair of figures, one larger than the other. For each pair, show that the two figures are similar by identifying a sequence of translations, rotations, reflections, and dilations that takes the smaller figure to the larger one.
![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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T003740Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d553b0b811a75618052d2b6f9073d06322aa40c8dc8bb92d975a8b8b20b1c410)
![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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T003740Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ac312033c05955bc03a9a71cd8e44378005e0b8f0c73d251e7fe714abfff8c45)
Solution
For access, consult one of our IM Certified Partners.
Problem 2
Here are two similar polygons.
Measure the side lengths and angles of each polygon. What do you notice?
![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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T003740Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=766139e75087a7339e7b1d6b445ec2089bcb82cbc4ea733e7c59b74a4a450e1d)
Solution
For access, consult one of our IM Certified Partners.
Problem 3
Each figure shows a pair of similar triangles, one contained in the other. For each pair, describe a point and a scale factor to use for a dilation moving the larger triangle to the smaller one. Use a measurement tool to find the scale factor.
![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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T003740Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=bab38be9346c54d193b34ebe75b77380dd30a8a531803f4ccfbcb2ba1a476187)
![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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T003740Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=2664963fa02fa7ee63676227353bb0f3d1f4e491d42ddbadeced94a2ba0c4a73)
Solution
For access, consult one of our IM Certified Partners.