1. If L and L' are parallel lines and t Z L is a line that t inters...

Question
1. If L and L' are parallel lines and t Z L is a line that t intersects L, than t also intersects L'.

2. If l is parallel to m & m is parallel to n than either l=n or l||n.

3. Show that for any triangle the sum of interior angles is 180.
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      • Illuminate\Cache\Events\CacheHit (429μs)
      • Illuminate\Cache\Events\CacheHit (1.67ms)
      • Illuminate\Cache\Events\CacheHit (311μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (664μs)
      • Illuminate\Cache\Events\CacheHit (252μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • creating: site.layouts.app (507μs)
      • composing: site.layouts.app (19μs)
      • creating: components.canonical (443μs)
      • composing: components.canonical (107μs)
      • creating: components.open-graph (485μs)
      • composing: components.open-graph (93μs)
      • creating: site.headers.header (334μs)
      • composing: site.headers.header (78μs)
      • Illuminate\Cache\Events\CacheHit (3.29ms)
      • creating: components.footer (103μs)
      • composing: components.footer (273μs)
      • Illuminate\Cache\Events\CacheHit (1.38ms)
      • Illuminate\Cache\Events\CacheMissed (459μs)
      • Illuminate\Database\Events\StatementPrepared (900μs)
      • Illuminate\Database\Events\QueryExecuted (1.15ms)
      • eloquent.retrieved: App\Models\SubjectCat (90μs)
      • Illuminate\Cache\Events\KeyWritten (1.56ms)
      • Illuminate\Cache\Events\CacheHit (572μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (1.53ms)
      • Illuminate\Cache\Events\CacheHit (1.09ms)
      • Illuminate\Cache\Events\CacheHit (334μs)
      • Illuminate\Cache\Events\CacheHit (326μs)
      • Illuminate\Cache\Events\CacheHit (272μs)
      • Illuminate\Cache\Events\CacheHit (330μs)
      • Illuminate\Cache\Events\CacheHit (327μs)
      • Illuminate\Cache\Events\CacheHit (229μs)
      • Illuminate\Cache\Events\CacheHit (392μs)
      • creating: components.forms.contact-us (236μs)
      • composing: components.forms.contact-us (156μs)
      • creating: components.forms.get-started (116μs)
      • composing: components.forms.get-started (74μs)
      • creating: components.forms.free-tool-download (104μs)
      • composing: components.forms.free-tool-download (68μs)
      • creating: components.forms.claim-free-worksheet (189μs)
      • composing: components.forms.claim-free-worksheet (75μs)
      • creating: components.forms.tutor-subscription-waitlist (112μs)
      • composing: components.forms.tutor-subscription-waitlist (109μs)
      • creating: components.forms.tutor-subscription-join (108μs)
      • composing: components.forms.tutor-subscription-join (67μs)
      • creating: components.forms.tutor-support (103μs)
      • composing: components.forms.tutor-support (66μs)
      • 311 x Illuminate\Cache\Events\CacheHit (17.76%)
        116ms
        20 x Illuminate\Database\Events\StatementPrepared (8.62%)
        56.27ms
        20 x Illuminate\Database\Events\QueryExecuted (4.31%)
        28.15ms
        11 x Illuminate\Cache\Events\KeyWritten (2%)
        13.04ms
        11 x Illuminate\Cache\Events\CacheMissed (1.69%)
        11.03ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.23%)
        1.51ms
        12 x eloquent.retrieved: App\Models\SubjectCat (0.2%)
        1.28ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.11%)
        709μs
        1 x Illuminate\Routing\Events\Routing (0.11%)
        701μs
        1 x creating: site.layouts.app (0.08%)
        507μs
        1 x creating: components.open-graph (0.07%)
        485μs
        1 x creating: components.canonical (0.07%)
        443μs
        1 x creating: homework.show (0.07%)
        442μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.06%)
        366μs
        1 x creating: components.breadcrumbs (0.05%)
        335μs
        1 x creating: site.headers.header (0.05%)
        334μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.05%)
        324μs
        1 x Illuminate\Routing\Events\RouteMatched (0.05%)
        324μs
        2 x eloquent.retrieved: App\Models\Subject (0.04%)
        283μs
        1 x eloquent.booting: App\Models\SubjectCat (0.04%)
        281μs
        1 x composing: components.footer (0.04%)
        273μs
        1 x creating: components.forms.contact-us (0.04%)
        236μs
        1 x creating: components.forms.claim-free-worksheet (0.03%)
        189μs
        1 x composing: components.forms.contact-us (0.02%)
        156μs
        1 x eloquent.booting: App\Models\Subject (0.02%)
        137μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.02%)
        136μs
        1 x composing: components.breadcrumbs (0.02%)
        131μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.02%)
        122μs
        1 x creating: components.forms.get-started (0.02%)
        116μs
        1 x composing: homework.show (0.02%)
        114μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.02%)
        112μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.02%)
        109μs
        1 x creating: components.forms.tutor-subscription-join (0.02%)
        108μs
        1 x composing: components.canonical (0.02%)
        107μs
        1 x creating: components.forms.free-tool-download (0.02%)
        104μs
        1 x creating: components.forms.tutor-support (0.02%)
        103μs
        1 x creating: components.footer (0.02%)
        103μs
        1 x composing: components.open-graph (0.01%)
        93μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        84μs
        1 x composing: site.headers.header (0.01%)
        78μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        75μs
        1 x composing: components.forms.get-started (0.01%)
        74μs
        1 x composing: components.forms.free-tool-download (0.01%)
        68μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        67μs
        1 x composing: components.forms.tutor-support (0.01%)
        66μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        62μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        62μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        46μs
        1 x composing: site.layouts.app (0%)
        19μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
      file
      app/Http/Controllers/HomeworkLibraryController.php:79-176
      20 statements were executed, 5 of which were duplicates, 15 unique. Show only duplicated66.38ms
      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#91
        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '17459' limit 1
        33.85mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 17459
        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (3)
        1.28mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (17459)
        2.63mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.22mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 17459 and `subject` = 3 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        3.24mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 17459
        • 1: 3
        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (3)
        1.19mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 17459 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.04mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 17459
        • 1: question
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 17459 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        1.18mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 17459
        • 1: teaser
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 17459 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        1.19mstwenty4_siteHomeworkLibrary.php#260
        Bindings
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        • 1: solution
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.09mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.36mstwenty4_siteSubject.php#100
        Bindings
        • 0: 1
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        1.08mstwenty4_siteSubject.php#100
        Bindings
        • 0: 3
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        1.04mstwenty4_siteSubject.php#100
        Bindings
        • 0: 4
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.1mstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1
        1.06mstwenty4_siteSubject.php#100
        Bindings
        • 0: 33
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1
        1.24mstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1
        1.29mstwenty4_siteSubject.php#100
        Bindings
        • 0: 5
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        7.27mstwenty4_siteSubject.php#100
        Bindings
        • 0: 34
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        1.76mstwenty4_siteSubject.php#100
        Bindings
        • 0: 31
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1
        1.27mstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 28. view::components.footer:170
      App\Models\SubjectCat
      12SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      7HomeworkLibraryFile.php
      App\Models\Subject
      2Subject.php
          _token
          tpxsMaYgpgXOPFRvh6F8OL1BgeSEwdQEMCh1a0A3
          utm_source
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          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Geo...
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          PHPDEBUGBAR_STACK_DATA
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          status_code
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          status_text
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          format
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          content_type
          text/html; charset=UTF-8
          request_query
          []
          
          request_request
          []
          
          request_headers
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          request_cookies
          []
          
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