Lesson 47 Congruence Transformations Video Notes
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=YlqXiatRTuc
Objectives: Identify reflections, translations, and rotations; Verify congruence after a congruence transformation.","styleRuns":[{"startIndex":0,"length":115,"styleRunExtensions":{"styleRunColorMapExtension":{"colorMap":[{"key":"USER_INTERFACE_THEME_DARK","value":4294967295},{"key":"USER_INTERFACE_THEME_LIGHT","value":4279440147}]}},"fontFamilyName":"Roboto"}]},"headerRuns":[{"startIndex":0,"length":115,"headerMapping":"ATTRIBUTED_STRING_HEADER_MAPPING_UNSPECIFIED"}]}},{"itemSectionRenderer":{"contents":[{"continuationItemRenderer":{"trigger":"CONTINUATION_TRIGGER_ON_ITEM_SHOWN","continuationEndpoint":{"clickTrackingParams":"CKEBELsvGAIiEwjV3o-4ksuLAxV-0EIFHeLsENw=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/next"}},"continuationCommand":{"token":"Eg0SC1lscVhpYXRSVHVjGAYyJSIRIgtZbHFYaWF0UlR1YzAAeAJCEGNvbW1lbnRzLXNlY3Rpb24%3D","request":"CONTINUATION_REQUEST_TYPE_WATCH_NEXT"}}}}],"trackingParams":"CKEBELsvGAIiEwjV3o-4ksuLAxV-0EIFHeLsENw=","sectionIdentifier":"comment-item-section","targetId":"comments-section"}}],"trackingParams":"CKABELovIhMI1d6PuJLLiwMVftBCBR3i7BDc"}},"secondaryResults":{"secondaryResults":{"results":[{"compactVideoRenderer":{"videoId":"shFUDPqVmTg","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/shFUDPqVmTg/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLD6trXqILbGZvDfopg9RuBzdTUVZQ","width":168,"height":94},{"url":"https://i.ytimg.com/vi/shFUDPqVmTg/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLC10h-S8C9WAL9JBIwhJueUC6D45g","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"I was asked to keep this confidential by Sabine Hossenfelder 1,749,791 views 2 days ago 9 minutes, 42 seconds"}},"simpleText":"I was asked to keep this confidential"},"longBylineText":{"runs":[{"text":"Sabine Hossenfelder","navigationEndpoint":{"clickTrackingParams":"CJkBEKQwGAAiEwjV3o-4ksuLAxV-0EIFHeLsENwyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@SabineHossenfelder","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC1yNl2E66ZzKApQdRuTQ4tw","canonicalBaseUrl":"/@SabineHossenfelder"}}}]},"publishedTimeText":{"simpleText":"2 days ago"},"viewCountText":{"simpleText":"1,749,791 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"9 minutes, 42 seconds"}},"simpleText":"9:42"},"navigationEndpoint":{"clickTrackingParams":"CJkBEKQwGAAiEwjV3o-4ksuLAxV-0EIFHeLsENwyB3JlbGF0ZWRI553F2prxpa1imgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=shFUDPqVmTg","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"shFUDPqVmTg","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr3---sn-nvm-cxbz.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=b211540cfa959938 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=860000 mt=1739809982 oweuc= pxtags=Cg4KAnR4Egg1MTM5MzE1Nw rxtags=Cg4KAnR4Egg1MTM5MzE1NA%2CCg4KAnR4Egg1MTM5MzE1NQ%2CCg4KAnR4Egg1MTM5MzE1Ng%2CCg4KAnR4Egg1MTM5MzE1Nw%2CCg4KAnR4Egg1MTM5MzE1OA"}}}}},"shortBylineText":{"runs":[{"text":"Sabine Hossenfelder","navigationEndpoint":{"clickTrackingParams":"CJkBEKQwGAAiEwjV3o-4ksuLAxV-0EIFHeLsENwyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@SabineHossenfelder","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC1yNl2E66ZzKApQdRuTQ4tw","canonicalBaseUrl":"/@SabineHossenfelder"}}}]},"badges":[{"metadataBadgeRenderer":{"style":"BADGE_STYLE_TYPE_SIMPLE","label":"New","trackingParams":"CJkBEKQwGAAiEwjV3o-4ksuLAxV-0EIFHeLsENw="}}],"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/YjHzJACT7jTFzpkHRfjWxmVKeBh6_8BpvVFS4iT8fb5xwoAU4sq1SeRGUju91bDOFJo6AjQMOZA=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"ownerBadges":[{"metadataBadgeRenderer":{"icon":{"iconType":"CHECK_CIRCLE_THICK"},"style":"BADGE_STYLE_TYPE_VERIFIED","tooltip":"Verified","trackingParams":"CJkBEKQwGAAiEwjV3o-4ksuLAxV-0EIFHeLsENw=","accessibilityData":{"label":"Verified"}}}],"trackingParams":"CJkBEKQwGAAiEwjV3o-4ksuLAxV-0EIFHeLsENxAuLLW1M-B1YiyAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"1.7 million views"}},"simpleText":"1.7M views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CJ4BEP6YBBgIIhMI1d6PuJLLiwMVftBCBR3i7BDc","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CJ4BEP6YBBgIIhMI1d6PuJLLiwMVftBCBR3i7BDc","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"shFUDPqVmTg","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CJ4BEP6YBBgIIhMI1d6PuJLLiwMVftBCBR3i7BDc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["shFUDPqVmTg"],"params":"CAQ%3D"}},"videoIds":["shFUDPqVmTg"]}},{"clickTrackingParams":"CJ4BEP6YBBgIIhMI1d6PuJLLiwMVftBCBR3i7BDc","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CJ8BELlqIhMI1d6PuJLLiwMVftBCBR3i7BDc"}},"popupType":"TOAST"}}]}},"trackingParams":"CJ4BEP6YBBgIIhMI1d6PuJLLiwMVftBCBR3i7BDc"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CJ0BENGqBRgJIhMI1d6PuJLLiwMVftBCBR3i7BDc","offlineVideoEndpoint":{"videoId":"shFUDPqVmTg","onAddCommand":{"clickTrackingParams":"CJ0BENGqBRgJIhMI1d6PuJLLiwMVftBCBR3i7BDc","getDownloadActionCommand":{"videoId":"shFUDPqVmTg","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CJ0BENGqBRgJIhMI1d6PuJLLiwMVftBCBR3i7BDc"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CJkBEKQwGAAiEwjV3o-4ksuLAxV-0EIFHeLsENw=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtzaEZVRFBxVm1UZw%3D%3D","commands":[{"clickTrackingParams":"CJkBEKQwGAAiEwjV3o-4ksuLAxV-0EIFHeLsENw=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CJwBEI5iIhMI1d6PuJLLiwMVftBCBR3i7BDc","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CJkBEKQwGAAiEwjV3o-4ksuLAxV-0EIFHeLsENw=","hasSeparator":true}}],"trackingParams":"CJkBEKQwGAAiEwjV3o-4ksuLAxV-0EIFHeLsENw=","accessibility":{"accessibilityData":{"label":"Action menu"}},"targetId":"watch-related-menu-button"}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"9 minutes, 42 seconds"}},"simpleText":"9:42"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CJsBEPnnAxgDIhMI1d6PuJLLiwMVftBCBR3i7BDc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"shFUDPqVmTg","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CJsBEPnnAxgDIhMI1d6PuJLLiwMVftBCBR3i7BDc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"shFUDPqVmTg"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CJsBEPnnAxgDIhMI1d6PuJLLiwMVftBCBR3i7BDc"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CJoBEMfsBBgEIhMI1d6PuJLLiwMVftBCBR3i7BDc","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CJoBEMfsBBgEIhMI1d6PuJLLiwMVftBCBR3i7BDc","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"shFUDPqVmTg","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CJoBEMfsBBgEIhMI1d6PuJLLiwMVftBCBR3i7BDc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["shFUDPqVmTg"],"params":"CAQ%3D"}},"videoIds":["shFUDPqVmTg"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CJoBEMfsBBgEIhMI1d6PuJLLiwMVftBCBR3i7BDc"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"I was asked to keep this confidential - 9 minutes, 42 seconds - Go to channel - Sabine Hossenfelder - 1.7M views - 2 days ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/shFUDPqVmTg/mqdefault_6s.webp?du=3000 sqp=CPi1zb0G rs=AOn4CLD0VV0yJNu-q18CcyrswckHjJUaWQ","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"pnzUVCnszcA","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/pnzUVCnszcA/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLCErsyIJhDErQr3PpUI7fa_mLWm-Q","width":168,"height":94},{"url":"https://i.ytimg.com/vi/pnzUVCnszcA/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLApfh6LrwJEbgBjXUEfVK2qqq9G2g","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"6 1 Properties and Attributes of Polygons by Wes Allred 898 views 9 years ago 15 minutes"}},"simpleText":"6 1 Properties and Attributes of Polygons"},"longBylineText":{"runs":[{"text":"Wes Allred","navigationEndpoint":{"clickTrackingParams":"CJIBEKQwGAEiEwjV3o-4ksuLAxV-0EIFHeLsENwyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@wesallred8798","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCciEEtamPxL6oUIzs79vD-A","canonicalBaseUrl":"/@wesallred8798"}}}]},"publishedTimeText":{"simpleText":"9 years ago"},"viewCountText":{"simpleText":"898 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"15 minutes, 2 seconds"}},"simpleText":"15:02"},"navigationEndpoint":{"clickTrackingParams":"CJIBEKQwGAEiEwjV3o-4ksuLAxV-0EIFHeLsENwyB3JlbGF0ZWRI553F2prxpa1imgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=pnzUVCnszcA","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"pnzUVCnszcA","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr3---sn-nvm-cxbz.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=a67cd45429eccdc0 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=860000 mt=1739809982 oweuc= pxtags=Cg4KAnR4Egg1MTM5MzE1Nw rxtags=Cg4KAnR4Egg1MTM5MzE1NA%2CCg4KAnR4Egg1MTM5MzE1NQ%2CCg4KAnR4Egg1MTM5MzE1Ng%2CCg4KAnR4Egg1MTM5MzE1Nw%2CCg4KAnR4Egg1MTM5MzE1OA"}}}}},"shortBylineText":{"runs":[{"text":"Wes Allred","navigationEndpoint":{"clickTrackingParams":"CJIBEKQwGAEiEwjV3o-4ksuLAxV-0EIFHeLsENwyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@wesallred8798","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCciEEtamPxL6oUIzs79vD-A","canonicalBaseUrl":"/@wesallred8798"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_kF1KRIZyR0zBYVLazxC0cNdzeP-DUVds8lLDlzpS0=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CJIBEKQwGAEiEwjV3o-4ksuLAxV-0EIFHeLsENxAwJuzz8KKtb6mAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"898 views"}},"simpleText":"898 views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CJcBEP6YBBgGIhMI1d6PuJLLiwMVftBCBR3i7BDc","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CJcBEP6YBBgGIhMI1d6PuJLLiwMVftBCBR3i7BDc","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"pnzUVCnszcA","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CJcBEP6YBBgGIhMI1d6PuJLLiwMVftBCBR3i7BDc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["pnzUVCnszcA"],"params":"CAQ%3D"}},"videoIds":["pnzUVCnszcA"]}},{"clickTrackingParams":"CJcBEP6YBBgGIhMI1d6PuJLLiwMVftBCBR3i7BDc","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CJgBELlqIhMI1d6PuJLLiwMVftBCBR3i7BDc"}},"popupType":"TOAST"}}]}},"trackingParams":"CJcBEP6YBBgGIhMI1d6PuJLLiwMVftBCBR3i7BDc"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CJYBENGqBRgHIhMI1d6PuJLLiwMVftBCBR3i7BDc","offlineVideoEndpoint":{"videoId":"pnzUVCnszcA","onAddCommand":{"clickTrackingParams":"CJYBENGqBRgHIhMI1d6PuJLLiwMVftBCBR3i7BDc","getDownloadActionCommand":{"videoId":"pnzUVCnszcA","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CJYBENGqBRgHIhMI1d6PuJLLiwMVftBCBR3i7BDc"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CJIBEKQwGAEiEwjV3o-4ksuLAxV-0EIFHeLsENw=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtwbnpVVkNuc3pjQQ%3D%3D","commands":[{"clickTrackingParams":"CJIBEKQwGAEiEwjV3o-4ksuLAxV-0EIFHeLsENw=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CJUBEI5iIhMI1d6PuJLLiwMVftBCBR3i7BDc","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CJIBEKQwGAEiEwjV3o-4ksuLAxV-0EIFHeLsENw=","hasSeparator":true}}],"trackingParams":"CJIBEKQwGAEiEwjV3o-4ksuLAxV-0EIFHeLsENw=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"15 minutes, 2 seconds"}},"simpleText":"15:02"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CJQBEPnnAxgBIhMI1d6PuJLLiwMVftBCBR3i7BDc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"pnzUVCnszcA","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CJQBEPnnAxgBIhMI1d6PuJLLiwMVftBCBR3i7BDc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"pnzUVCnszcA"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CJQBEPnnAxgBIhMI1d6PuJLLiwMVftBCBR3i7BDc"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CJMBEMfsBBgCIhMI1d6PuJLLiwMVftBCBR3i7BDc","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CJMBEMfsBBgCIhMI1d6PuJLLiwMVftBCBR3i7BDc","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"pnzUVCnszcA","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CJMBEMfsBBgCIhMI1d6PuJLLiwMVftBCBR3i7BDc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["pnzUVCnszcA"],"params":"CAQ%3D"}},"videoIds":["pnzUVCnszcA"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CJMBEMfsBBgCIhMI1d6PuJLLiwMVftBCBR3i7BDc"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"6 1 Properties and Attributes of Polygons - 15 minutes - Go to channel - Wes Allred - 898 views - 9 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/pnzUVCnszcA/mqdefault_6s.webp?du=3000 sqp=COCCzb0G rs=AOn4CLCw6iy4_EDH0AXV06yybPm7VW4kHQ","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"EgpzBDI5VAA","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/EgpzBDI5VAA/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLCtowkxEcunsQFTP4kGo9_fkVSr9Q","width":168,"height":94},{"url":"https://i.ytimg.com/vi/EgpzBDI5VAA/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLBwXSlQG3ATnMy-pHq8NFOWlPNOnA","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Proving Conjectures - Deductive Reasoning by Mr Howell's Math 5,829 views 6 years ago 5 minutes, 28 seconds"}},"simpleText":"Proving Conjectures - Deductive Reasoning"},"longBylineText":{"runs":[{"text":"Mr Howell's Math","navigationEndpoint":{"clickTrackingParams":"CIsBEKQwGAIiEwjV3o-4ksuLAxV-0EIFHeLsENwyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@gahowell1","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCF7yRXA3pMQAqN6F-jDfOog","canonicalBaseUrl":"/@gahowell1"}}}]},"publishedTimeText":{"simpleText":"6 years ago"},"viewCountText":{"simpleText":"5,829 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"5 minutes, 28 seconds"}},"simpleText":"5:28"},"navigationEndpoint":{"clickTrackingParams":"CIsBEKQwGAIiEwjV3o-4ksuLAxV-0EIFHeLsENwyB3JlbGF0ZWRI553F2prxpa1imgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=EgpzBDI5VAA","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"EgpzBDI5VAA","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr3---sn-nv47lns7.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=120a730432395400 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=922500 mt=1739809982 oweuc= pxtags=Cg4KAnR4Egg1MTM5MzE1Nw rxtags=Cg4KAnR4Egg1MTM5MzE1NA%2CCg4KAnR4Egg1MTM5MzE1NQ%2CCg4KAnR4Egg1MTM5MzE1Ng%2CCg4KAnR4Egg1MTM5MzE1Nw%2CCg4KAnR4Egg1MTM5MzE1OA"}}}}},"shortBylineText":{"runs":[{"text":"Mr Howell's Math","navigationEndpoint":{"clickTrackingParams":"CIsBEKQwGAIiEwjV3o-4ksuLAxV-0EIFHeLsENwyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@gahowell1","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCF7yRXA3pMQAqN6F-jDfOog","canonicalBaseUrl":"/@gahowell1"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/D7k16AgNV5sl5XKme5NK5s4J-ce1b9-gmHafoy0zW3vbUI6fTbGwrvimhF3Ebrn1kdF6aN0QRQ=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CIsBEKQwGAIiEwjV3o-4ksuLAxV-0EIFHeLsENxAgKjlkcPgnIUS","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"5.8K views"}},"simpleText":"5.8K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CJABEP6YBBgFIhMI1d6PuJLLiwMVftBCBR3i7BDc","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CJABEP6YBBgFIhMI1d6PuJLLiwMVftBCBR3i7BDc","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"EgpzBDI5VAA","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CJABEP6YBBgFIhMI1d6PuJLLiwMVftBCBR3i7BDc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["EgpzBDI5VAA"],"params":"CAQ%3D"}},"videoIds":["EgpzBDI5VAA"]}},{"clickTrackingParams":"CJABEP6YBBgFIhMI1d6PuJLLiwMVftBCBR3i7BDc","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CJEBELlqIhMI1d6PuJLLiwMVftBCBR3i7BDc"}},"popupType":"TOAST"}}]}},"trackingParams":"CJABEP6YBBgFIhMI1d6PuJLLiwMVftBCBR3i7BDc"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CI8BENGqBRgGIhMI1d6PuJLLiwMVftBCBR3i7BDc","offlineVideoEndpoint":{"videoId":"EgpzBDI5VAA","onAddCommand":{"clickTrackingParams":"CI8BENGqBRgGIhMI1d6PuJLLiwMVftBCBR3i7BDc","getDownloadActionCommand":{"videoId":"EgpzBDI5VAA","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CI8BENGqBRgGIhMI1d6PuJLLiwMVftBCBR3i7BDc"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CIsBEKQwGAIiEwjV3o-4ksuLAxV-0EIFHeLsENw=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtFZ3B6QkRJNVZBQQ%3D%3D","commands":[{"clickTrackingParams":"CIsBEKQwGAIiEwjV3o-4ksuLAxV-0EIFHeLsENw=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CI4BEI5iIhMI1d6PuJLLiwMVftBCBR3i7BDc","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CIsBEKQwGAIiEwjV3o-4ksuLAxV-0EIFHeLsENw=","hasSeparator":true}}],"trackingParams":"CIsBEKQwGAIiEwjV3o-4ksuLAxV-0EIFHeLsENw=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"5 minutes, 28 seconds"}},"simpleText":"5:28"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CI0BEPnnAxgBIhMI1d6PuJLLiwMVftBCBR3i7BDc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"EgpzBDI5VAA","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CI0BEPnnAxgBIhMI1d6PuJLLiwMVftBCBR3i7BDc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"EgpzBDI5VAA"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CI0BEPnnAxgBIhMI1d6PuJLLiwMVftBCBR3i7BDc"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CIwBEMfsBBgCIhMI1d6PuJLLiwMVftBCBR3i7BDc","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CIwBEMfsBBgCIhMI1d6PuJLLiwMVftBCBR3i7BDc","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"EgpzBDI5VAA","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CIwBEMfsBBgCIhMI1d6PuJLLiwMVftBCBR3i7BDc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["EgpzBDI5VAA"],"params":"CAQ%3D"}},"videoIds":["EgpzBDI5VAA"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CIwBEMfsBBgCIhMI1d6PuJLLiwMVftBCBR3i7BDc"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Proving Conjectures - Deductive Reasoning - 5 minutes, 28 seconds - Go to channel - Mr Howell's Math - 5.8K views - 6 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"lockupViewModel":{"contentImage":{"collectionThumbnailViewModel":{"primaryThumbnail":{"thumbnailViewModel":{"image":{"sources":[{"url":"https://i.ytimg.com/vi/pTVgvpizTCk/hqdefault.jpg?sqp=-oaymwEWCKgBEF5IWvKriqkDCQgBFQAAiEIYAQ== rs=AOn4CLDHpgo4iY_1kBHZfVIpt8V0oJaGEQ","width":168,"height":94},{"url":"https://i.ytimg.com/vi/pTVgvpizTCk/hqdefault.jpg?sqp=-oaymwEXCNACELwBSFryq4qpAwkIARUAAIhCGAE= rs=AOn4CLDSFptFG16lEXhN82riDyHYsnpayg","width":336,"height":188}]},"overlays":[{"thumbnailOverlayBadgeViewModel":{"thumbnailBadges":[{"thumbnailBadgeViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAYLISTS"}}]},"text":"172 videos","badgeStyle":"THUMBNAIL_OVERLAY_BADGE_STYLE_DEFAULT","backgroundColor":{"lightTheme":1386010,"darkTheme":1386010}}}],"position":"THUMBNAIL_OVERLAY_BADGE_POSITION_BOTTOM_END"}},{"thumbnailHoverOverlayViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAY_ALL"}}]},"text":{"content":"Play all","styleRuns":[{"startIndex":0,"length":8}]},"style":"THUMBNAIL_HOVER_OVERLAY_STYLE_COVER"}}],"backgroundColor":{"lightTheme":2309931,"darkTheme":2309931}}},"stackColor":{"lightTheme":7051639,"darkTheme":7375991}}},"metadata":{"lockupMetadataViewModel":{"title":{"content":"Square Roots and Powers and Exponents"},"metadata":{"contentMetadataViewModel":{"metadataRows":[{"metadataParts":[{"text":{"content":"TabletClass Math
#############################
![](http://youtor.org/essay_main.png)