https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-trans-and-congruence/v/testing-congruence-by-transformations-example 2023-05-12T21:01:01.897246564Z Congruent shapes & transformations If we can map one figure onto another using rigid transformations, they are congruent. They are still congruent if we need to use more than one transformation to map it. They aren't if we use a transformation that changes the size of the shape. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/7811ba8e-b490-41c7-be51-5bdf6b3e2c2b_1280_720_base.png Congruent shapes & transformations If we can map one figure onto another using rigid transformations, they are congruent. They are still congruent if we need to use more than one transformation to map it. They aren't if we use a transformation that changes the size of the shape. https://cdn.kastatic.org/ka-youtube-converted/KZMRhWdzEPo.mp4/KZMRhWdzEPo.mp4 103 Congruence & similarity https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-trans-and-congruence/v/another-congruence-by-transformation-example 2023-05-12T21:01:01.897246564Z Non-congruent shapes & transformations Congruent shapes are the same size and shape. Rigid transformations, like translations, keep shapes congruent, but dilations are not rigid transformations because they change the size. So, if we use a dilation to map one shape onto another, they are not congruent. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/84ef4bd1-59c1-4e52-b429-88353c17c18c_1280_720_base.png Non-congruent shapes & transformations Congruent shapes are the same size and shape. Rigid transformations, like translations, keep shapes congruent, but dilations are not rigid transformations because they change the size. So, if we use a dilation to map one shape onto another, they are not congruent. https://cdn.kastatic.org/ka-youtube-converted/7Rb3V-HyVD8.mp4/7Rb3V-HyVD8.mp4 123 Congruence & similarity https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-trans-and-congruence/e/exploring-rigid-transformations-and-congruence 2026-06-16T15:15:41.378310859Z Congruence & transformations Given a pair of figures in the coordinate plane, determine whether they are congruent based on whether it is possible to map one to the other using rigid transformations. Sandy Knight exercise https://www.khanacademy.org/math/geometry/hs-geo-similarity/hs-geo-similarity-definitions/v/testing-similarity-through-transformations 2023-05-12T21:01:01.897246564Z Similar shapes & transformations Two shapes are similar if we can change one shape into the other using rigid transformations (like moving or rotating) and dilations (making it bigger or smaller). Other kinds of transformations can change the angles or the ratios of lengths in a figure. If we need those types of transformations, the shapes are not similar. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/95165e7e-8131-4ac8-a2d0-7ee788f53bf6_1280_720_base.png Similar shapes & transformations Two shapes are similar if we can change one shape into the other using rigid transformations (like moving or rotating) and dilations (making it bigger or smaller). Other kinds of transformations can change the angles or the ratios of lengths in a figure. If we need those types of transformations, the shapes are not similar. https://cdn.kastatic.org/ka-youtube-converted/H-YuW_uckz4.mp4/H-YuW_uckz4.mp4 158 Congruence & similarity https://www.khanacademy.org/math/geometry/hs-geo-similarity/hs-geo-similarity-definitions/e/exploring-angle-preserving-transformations-and-similarity 2026-03-09T04:30:46.094426574Z Similarity & transformations Given a pair of figures in the coordinate plane, determine whether they are similar based on whether it is possible to map one to the other using angle-preserving transformations. Tomer Gal exercise https://www.khanacademy.org/math/cc-eighth-grade-math/geometric-transformations/congruence-similarity/v/comparing-side-lengths-after-dilation 2023-05-12T21:01:01.897246564Z Side lengths after dilation In a dilation, if the scale factor is greater than 1, the shape will stretch away from the center of dilation, getting larger. If the scale factor is between 0 and 1, the shape will shrink towards the center, getting smaller. All the lengths in the figure change by the same scale factor. Sal Khan video https://cdn.kastatic.org/googleusercontent/1tqAysCkWMsaZaQ8XcJR9tFjMROLNFS4iICLspGd-KAyTupVCVlXT-h1KCFCA69M32KrH3mTt9q9jpFSR0VNAJI Side lengths after dilation In a dilation, if the scale factor is greater than 1, the shape will stretch away from the center of dilation, getting larger. If the scale factor is between 0 and 1, the shape will shrink towards the center, getting smaller. All the lengths in the figure change by the same scale factor. https://cdn.kastatic.org/ka-youtube-converted/2yjSAarzWF8.mp4/2yjSAarzWF8.mp4 133 Congruence & similarity