| 1. |
info: 2025-04-26 00:57:50.409 RelationalEventId.CommandExecuted[20101] (Microsoft.EntityFrameworkCore.Database.Command)
21ms [Parameters=[@p7='d3a5b752-2ac9-4e00-8a3a-c9fde6cad3d4', @p0='True', @p1='False', @p2='3', @p3='02c5c9c6-d959-466f-b3ae-b25fc50031bf', @p4='201.jpg' (Size = 100), @p5='https://knowledgenest.blob.core.windows.net/scanners/0/[Matematika][Horizontai Matematika 9 klasė][Vadovėlis 1 dalis]/pages/201.jpg' (Size = 1000), @p6='## 4
a) O - apskritimo centras, AB - skersmuo. Taškai C ir D parinkti taip, kad ◡AD = ◡BC. Įrodykite, kad: 1) △ABC ~ △ABD; 2) △ABC = △ABD.
**Duota:** O - apskritimo centras, AB - skersmuo, ◡AD = ◡BC.
**Įrodyti:** 1) △ABC ~ △ABD; 2) △ABC = △ABD.
**Įrodymas**
1) ∠CAB = ∠ABD, nes įbrėžtiniai kampai kerta vienodo dydžio lankus.
∠ADB = ∠ACB = ......... , nes ......... .
△ABC ~ △ABD pagal du lygius kampus:
.........
.........
**Įrodyta.**
2) ∠CBA = ∠DAB, nes jeigu trikampių du kampai atitinkamai lygūs, tai tretieji kampai irgi lygūs.
△ABC = △ABD pagal kraštinę ir du kampus prie jos:
* AB - bendra kraštinė,
* ∠CAB = ∠ABD, nes įbrėžtiniai kampai kerta vienodo dydžio lankus.
* ∠CBA = ∠DAB.
**Įrodyta.**
b) Apskritimo stygos AB ir CD susikerta taške E. Nubraižykite brėžinį ir įrodykite, kad △ACE ~ △DBE.
## 5
a) Apskritimą kerta dvi lygiagrečios tiesės BC ir AD. AD - apskritimo skersmuo. Įrodykite, kad AB = CD.
**Duota:** BC || AD, AD - apskritimo skersmuo.
**Įrodyti:** AB = CD.
**Įrodymas**
1) Brėžiame OB ir OC.
2) Trikampiai ABO, BOC ir CDO yra lygiašoniai, nes AO = BO = CO = DO = R.
3) ∠OBC = ∠OCB = α, nes lygiašonio trikampio kampai prie pagrindo yra lygūs.
4) ∠OBC = ∠BOA = α, nes vidaus priešiniai kampai lygūs.
∠BCO = ∠COD = α, nes ......... .
5) △ABO = △DCO pagal dvi lygias kraštines ir kampą tarp jų:
.........
.........
6) AB = CD, nes ......... trikampių atitinkamos ......... yra lygios.
**Įrodyta.**' (Size = 4000)], CommandType='Text', CommandTimeout='30']
SET IMPLICIT_TRANSACTIONS OFF;
SET NOCOUNT ON;
UPDATE [ScannerPages] SET [Active] = @p0, [Deleted] = @p1, [Position] = @p2, [ScannerId] = @p3, [StorageMediaName] = @p4, [StorageMediaUrl] = @p5, [Text] = @p6
OUTPUT 1
WHERE [Id] = @p7;
|
| 2. |
info: 2025-04-26 00:57:50.521 RelationalEventId.CommandExecuted[20101] (Microsoft.EntityFrameworkCore.Database.Command)
2ms [Parameters=[@__id_0='29f9ef45-04b0-a1a9-bf04-37350936373b', @__site_Id_1='63d6eb4e-8e39-4ac6-8f69-55ee76feccce'], CommandType='Text', CommandTimeout='30']
SELECT [c].[Id], [c].[Active], [c].[Deleted], [c].[Description], [c].[DescriptionBackup], [c].[Left], [c].[ParentId], [c].[Position], [c].[ProcessorGenerateImagePrompt], [c].[Right], [c].[SiteId], [c].[StorageMediaName], [c].[StorageMediaUrl], [c].[Title], [c].[TitleBackup], [c].[TitleSlug], [c].[TotalChildren], [c].[TotalScanners], [c].[TotalYoutubeVideos]
FROM [Categories] AS [c] WITH (NOLOCK)
WHERE [c].[Id] = @__id_0 AND [c].[SiteId] = @__site_Id_1 AND [c].[Active] = CAST(1 AS bit) AND [c].[Deleted] = CAST(0 AS bit)
ORDER BY [c].[Id]
|
| 3. |
info: 2025-04-26 00:57:50.528 RelationalEventId.CommandExecuted[20101] (Microsoft.EntityFrameworkCore.Database.Command)
7ms [Parameters=[@__id_0='29f9ef45-04b0-a1a9-bf04-37350936373b', @__site_Id_1='63d6eb4e-8e39-4ac6-8f69-55ee76feccce'], CommandType='Text', CommandTimeout='30']
SELECT [c4].[Id], [c4].[Active], [c4].[Deleted], [c4].[Description], [c4].[DescriptionBackup], [c4].[Left], [c4].[ParentId], [c4].[Position], [c4].[ProcessorGenerateImagePrompt], [c4].[Right], [c4].[SiteId], [c4].[StorageMediaName], [c4].[StorageMediaUrl], [c4].[Title], [c4].[TitleBackup], [c4].[TitleSlug], [c4].[TotalChildren], [c4].[TotalScanners], [c4].[TotalYoutubeVideos], [c].[Id]
FROM [Categories] AS [c] WITH (NOLOCK)
INNER JOIN (
SELECT [c0].[Id], [c0].[Active], [c0].[Deleted], [c0].[Description], [c0].[DescriptionBackup], [c0].[Left], [c0].[ParentId], [c0].[Position], [c0].[ProcessorGenerateImagePrompt], [c0].[Right], [c0].[SiteId], [c0].[StorageMediaName], [c0].[StorageMediaUrl], [c0].[Title], [c0].[TitleBackup], [c0].[TitleSlug], [c0].[TotalChildren], [c0].[TotalScanners], [c0].[TotalYoutubeVideos]
FROM [Categories] AS [c0] WITH (NOLOCK)
WHERE [c0].[Active] = CAST(1 AS bit) AND [c0].[Deleted] = CAST(0 AS bit)
) AS [c4] ON [c].[Id] = [c4].[ParentId]
WHERE [c].[Id] = @__id_0 AND [c].[SiteId] = @__site_Id_1 AND [c].[Active] = CAST(1 AS bit) AND [c].[Deleted] = CAST(0 AS bit)
ORDER BY [c].[Id], [c4].[Position], [c4].[Id]
|
| 4. |
info: 2025-04-26 00:57:50.530 RelationalEventId.CommandExecuted[20101] (Microsoft.EntityFrameworkCore.Database.Command)
2ms [Parameters=[@__id_0='29f9ef45-04b0-a1a9-bf04-37350936373b', @__site_Id_1='63d6eb4e-8e39-4ac6-8f69-55ee76feccce'], CommandType='Text', CommandTimeout='30']
SELECT [s5].[ScannerId], [s5].[CategoryId], [s5].[Id], [s5].[Active], [s5].[CheatSheet], [s5].[CheatSheet2], [s5].[Deleted], [s5].[FactErrors], [s5].[FactErrorsExplanation], [s5].[ParentCategory2Id], [s5].[ParentCategoryId], [s5].[ProcessorGenerateImagePrompt], [s5].[Prompt], [s5].[Reference], [s5].[ReferenceSlug], [s5].[SiteId], [s5].[SpellingErrors], [s5].[SpellingErrorsExplanation], [s5].[Summary], [s5].[Title], [s5].[TitleBackup], [s5].[TitleSlug], [s5].[TotalCards], [s5].[TotalCards2], [s5].[TotalCategories], [s5].[TotalPages], [s5].[Verified], [c].[Id]
FROM [Categories] AS [c] WITH (NOLOCK)
INNER JOIN (
SELECT [c3].[ScannerId], [c3].[CategoryId], [s1].[Id], [s1].[Active], [s1].[CheatSheet], [s1].[CheatSheet2], [s1].[Deleted], [s1].[FactErrors], [s1].[FactErrorsExplanation], [s1].[ParentCategory2Id], [s1].[ParentCategoryId], [s1].[ProcessorGenerateImagePrompt], [s1].[Prompt], [s1].[Reference], [s1].[ReferenceSlug], [s1].[SiteId], [s1].[SpellingErrors], [s1].[SpellingErrorsExplanation], [s1].[Summary], [s1].[Title], [s1].[TitleBackup], [s1].[TitleSlug], [s1].[TotalCards], [s1].[TotalCards2], [s1].[TotalCategories], [s1].[TotalPages], [s1].[Verified]
FROM [CategoryScanners] AS [c3]
INNER JOIN [Scanners] AS [s1] ON [c3].[ScannerId] = [s1].[Id]
WHERE [s1].[Active] = CAST(1 AS bit) AND [s1].[Deleted] = CAST(0 AS bit)
) AS [s5] ON [c].[Id] = [s5].[CategoryId]
WHERE [c].[Id] = @__id_0 AND [c].[SiteId] = @__site_Id_1 AND [c].[Active] = CAST(1 AS bit) AND [c].[Deleted] = CAST(0 AS bit)
ORDER BY [c].[Id], [s5].[Id], [s5].[ScannerId], [s5].[CategoryId]
|
| 5. |
info: 2025-04-26 00:57:50.542 RelationalEventId.CommandExecuted[20101] (Microsoft.EntityFrameworkCore.Database.Command)
2ms [Parameters=[@__id_0='29f9ef45-04b0-a1a9-bf04-37350936373b', @__site_Id_1='63d6eb4e-8e39-4ac6-8f69-55ee76feccce'], CommandType='Text', CommandTimeout='30']
SELECT [s6].[Id], [s6].[Active], [s6].[Context], [s6].[ContextBackup], [s6].[ContextStorageMediaName], [s6].[ContextStorageMediaUrl], [s6].[Deleted], [s6].[FactErrors], [s6].[FactErrorsExplanation], [s6].[Facts], [s6].[FactsBackup], [s6].[FactsStorageMediaName], [s6].[FactsStorageMediaUrl], [s6].[Position], [s6].[ProcessorGenerateImagePrompt], [s6].[Prompt], [s6].[ScannerId], [s6].[SpellingErrors], [s6].[SpellingErrorsExplanation], [s6].[StorageMediaName], [s6].[StorageMediaUrl], [s6].[Summary], [s6].[SummaryBackup], [s6].[SummaryStorageMediaName], [s6].[SummaryStorageMediaUrl], [s6].[Title], [s6].[TitleSlug], [s6].[TotalFillTheBlankSelectionQuestions], [s6].[TotalMultipleSelectionQuestions], [s6].[TotalOrderingQuestions], [s6].[TotalQuestionPoints], [s6].[TotalQuestions], [s6].[TotalShortAnswerQuestions], [s6].[TotalSingleSelectionQuestions], [s6].[TotalSources], [s6].[TotalTrueFalseQuestions], [s6].[Verified], [s6].[Version], [c].[Id], [s5].[ScannerId], [s5].[CategoryId], [s5].[Id]
FROM [Categories] AS [c] WITH (NOLOCK)
INNER JOIN (
SELECT [c3].[ScannerId], [c3].[CategoryId], [s1].[Id]
FROM [CategoryScanners] AS [c3]
INNER JOIN [Scanners] AS [s1] ON [c3].[ScannerId] = [s1].[Id]
WHERE [s1].[Active] = CAST(1 AS bit) AND [s1].[Deleted] = CAST(0 AS bit)
) AS [s5] ON [c].[Id] = [s5].[CategoryId]
INNER JOIN (
SELECT [s2].[Id], [s2].[Active], [s2].[Context], [s2].[ContextBackup], [s2].[ContextStorageMediaName], [s2].[ContextStorageMediaUrl], [s2].[Deleted], [s2].[FactErrors], [s2].[FactErrorsExplanation], [s2].[Facts], [s2].[FactsBackup], [s2].[FactsStorageMediaName], [s2].[FactsStorageMediaUrl], [s2].[Position], [s2].[ProcessorGenerateImagePrompt], [s2].[Prompt], [s2].[ScannerId], [s2].[SpellingErrors], [s2].[SpellingErrorsExplanation], [s2].[StorageMediaName], [s2].[StorageMediaUrl], [s2].[Summary], [s2].[SummaryBackup], [s2].[SummaryStorageMediaName], [s2].[SummaryStorageMediaUrl], [s2].[Title], [s2].[TitleSlug], [s2].[TotalFillTheBlankSelectionQuestions], [s2].[TotalMultipleSelectionQuestions], [s2].[TotalOrderingQuestions], [s2].[TotalQuestionPoints], [s2].[TotalQuestions], [s2].[TotalShortAnswerQuestions], [s2].[TotalSingleSelectionQuestions], [s2].[TotalSources], [s2].[TotalTrueFalseQuestions], [s2].[Verified], [s2].[Version]
FROM [ScannerCards] AS [s2]
WHERE [s2].[Active] = CAST(1 AS bit) AND [s2].[Deleted] = CAST(0 AS bit)
) AS [s6] ON [s5].[Id] = [s6].[ScannerId]
WHERE [c].[Id] = @__id_0 AND [c].[SiteId] = @__site_Id_1 AND [c].[Active] = CAST(1 AS bit) AND [c].[Deleted] = CAST(0 AS bit)
ORDER BY [c].[Id], [s5].[Id], [s5].[ScannerId], [s5].[CategoryId], [s6].[TitleSlug], [s6].[Id]
|
| 6. |
info: 2025-04-26 00:57:50.551 RelationalEventId.CommandExecuted[20101] (Microsoft.EntityFrameworkCore.Database.Command)
2ms [Parameters=[@__id_0='29f9ef45-04b0-a1a9-bf04-37350936373b', @__site_Id_1='63d6eb4e-8e39-4ac6-8f69-55ee76feccce'], CommandType='Text', CommandTimeout='30']
SELECT [q0].[Id], [q0].[Active], [q0].[Created], [q0].[Deleted], [q0].[Points], [q0].[ProcessorGenerateImagePrompt], [q0].[ScannerCardId], [q0].[StorageMediaName], [q0].[StorageMediaUrl], [q0].[Title], [q0].[TotalAnswers], [q0].[Type], [c].[Id], [s5].[ScannerId], [s5].[CategoryId], [s5].[Id], [s6].[Id]
FROM [Categories] AS [c] WITH (NOLOCK)
INNER JOIN (
SELECT [c3].[ScannerId], [c3].[CategoryId], [s1].[Id]
FROM [CategoryScanners] AS [c3]
INNER JOIN [Scanners] AS [s1] ON [c3].[ScannerId] = [s1].[Id]
WHERE [s1].[Active] = CAST(1 AS bit) AND [s1].[Deleted] = CAST(0 AS bit)
) AS [s5] ON [c].[Id] = [s5].[CategoryId]
INNER JOIN (
SELECT [s2].[Id], [s2].[ScannerId], [s2].[TitleSlug]
FROM [ScannerCards] AS [s2]
WHERE [s2].[Active] = CAST(1 AS bit) AND [s2].[Deleted] = CAST(0 AS bit)
) AS [s6] ON [s5].[Id] = [s6].[ScannerId]
INNER JOIN (
SELECT [q].[Id], [q].[Active], [q].[Created], [q].[Deleted], [q].[Points], [q].[ProcessorGenerateImagePrompt], [q].[ScannerCardId], [q].[StorageMediaName], [q].[StorageMediaUrl], [q].[Title], [q].[TotalAnswers], [q].[Type]
FROM [Questions] AS [q]
WHERE [q].[Active] = CAST(1 AS bit) AND [q].[Deleted] = CAST(0 AS bit)
) AS [q0] ON [s6].[Id] = [q0].[ScannerCardId]
WHERE [c].[Id] = @__id_0 AND [c].[SiteId] = @__site_Id_1 AND [c].[Active] = CAST(1 AS bit) AND [c].[Deleted] = CAST(0 AS bit)
ORDER BY [c].[Id], [s5].[Id], [s5].[ScannerId], [s5].[CategoryId], [s6].[TitleSlug], [s6].[Id], [q0].[Id]
|
| 7. |
info: 2025-04-26 00:57:50.561 RelationalEventId.CommandExecuted[20101] (Microsoft.EntityFrameworkCore.Database.Command)
7ms [Parameters=[@__id_0='29f9ef45-04b0-a1a9-bf04-37350936373b', @__site_Id_1='63d6eb4e-8e39-4ac6-8f69-55ee76feccce'], CommandType='Text', CommandTimeout='30']
SELECT [s7].[TagId], [s7].[ScannerCardId], [s7].[Id], [s7].[Active], [s7].[Created], [s7].[Deleted], [s7].[Description], [s7].[Links], [s7].[MediaSourceCopyright], [s7].[MediaSourceUrl], [s7].[ShortDescription], [s7].[SiteId], [s7].[StorageMediaName], [s7].[StorageMediaUrl], [s7].[Title], [s7].[TitleSlug], [s7].[Url], [s7].[Wikipedia], [s7].[WikipediaPageId], [s7].[WikipediaUpdated], [c].[Id], [s5].[ScannerId], [s5].[CategoryId], [s5].[Id], [s6].[Id]
FROM [Categories] AS [c] WITH (NOLOCK)
INNER JOIN (
SELECT [c3].[ScannerId], [c3].[CategoryId], [s1].[Id]
FROM [CategoryScanners] AS [c3]
INNER JOIN [Scanners] AS [s1] ON [c3].[ScannerId] = [s1].[Id]
WHERE [s1].[Active] = CAST(1 AS bit) AND [s1].[Deleted] = CAST(0 AS bit)
) AS [s5] ON [c].[Id] = [s5].[CategoryId]
INNER JOIN (
SELECT [s2].[Id], [s2].[ScannerId], [s2].[TitleSlug]
FROM [ScannerCards] AS [s2]
WHERE [s2].[Active] = CAST(1 AS bit) AND [s2].[Deleted] = CAST(0 AS bit)
) AS [s6] ON [s5].[Id] = [s6].[ScannerId]
INNER JOIN (
SELECT [t].[TagId], [t].[ScannerCardId], [t0].[Id], [t0].[Active], [t0].[Created], [t0].[Deleted], [t0].[Description], [t0].[Links], [t0].[MediaSourceCopyright], [t0].[MediaSourceUrl], [t0].[ShortDescription], [t0].[SiteId], [t0].[StorageMediaName], [t0].[StorageMediaUrl], [t0].[Title], [t0].[TitleSlug], [t0].[Url], [t0].[Wikipedia], [t0].[WikipediaPageId], [t0].[WikipediaUpdated]
FROM [TagScannerCards] AS [t]
INNER JOIN [Tags] AS [t0] ON [t].[TagId] = [t0].[Id]
WHERE [t0].[Active] = CAST(1 AS bit) AND [t0].[Deleted] = CAST(0 AS bit)
) AS [s7] ON [s6].[Id] = [s7].[ScannerCardId]
WHERE [c].[Id] = @__id_0 AND [c].[SiteId] = @__site_Id_1 AND [c].[Active] = CAST(1 AS bit) AND [c].[Deleted] = CAST(0 AS bit)
ORDER BY [c].[Id], [s5].[Id], [s5].[ScannerId], [s5].[CategoryId], [s6].[TitleSlug], [s6].[Id], [s7].[TitleSlug]
|
| 8. |
info: 2025-04-26 00:57:50.639 RelationalEventId.CommandExecuted[20101] (Microsoft.EntityFrameworkCore.Database.Command)
4ms [Parameters=[@__site_Id_0='63d6eb4e-8e39-4ac6-8f69-55ee76feccce', @__item_Left_1='2476', @__item_Right_2='2477'], CommandType='Text', CommandTimeout='30']
SELECT [c].[Id], [c].[Active], [c].[Deleted], [c].[Description], [c].[DescriptionBackup], [c].[Left], [c].[ParentId], [c].[Position], [c].[ProcessorGenerateImagePrompt], [c].[Right], [c].[SiteId], [c].[StorageMediaName], [c].[StorageMediaUrl], [c].[Title], [c].[TitleBackup], [c].[TitleSlug], [c].[TotalChildren], [c].[TotalScanners], [c].[TotalYoutubeVideos]
FROM [Categories] AS [c] WITH (NOLOCK)
WHERE [c].[SiteId] = @__site_Id_0 AND [c].[Left] <= @__item_Left_1 AND [c].[Right] >= @__item_Right_2 AND [c].[Deleted] = CAST(0 AS bit)
ORDER BY [c].[Left]
|
| 47 ms |
