User:Bawolff/sandbox
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This is the user sandbox of Bawolff. A user sandbox is a subpage of the user's user page. It serves as a testing spot and page development space for the user and is not an encyclopedia article. Create or edit your own sandbox here. Other sandboxes: Main sandbox | Template sandbox Finished writing a draft article? Are you ready to request review of it by an experienced editor for possible inclusion in Wikipedia? Submit your draft for review! |
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Let be a triangle.
The altitudes and intersect at .
We will show that also is perpendicular to , i.e. that it is an altitude of .
• The quadrilateral is cyclic, because .So, also (as angles subtended by the same arc).
• The quadrilateral is cyclic because opposite angles and are supplementary (since ). So, angles and are equal.
• The angles and are equal as vertical angles, i.e. . In the right triangle , we have that , therefore in the triangle it holds that .
We conclude that the three altitudes pass through the same point.
This is the user sandbox of Bawolff. A user sandbox is a subpage of the user's user page. It serves as a testing spot and page development space for the user and is not an encyclopedia article. Create or edit your own sandbox here. Other sandboxes: Main sandbox | Template sandbox Finished writing a draft article? Are you ready to request review of it by an experienced editor for possible inclusion in Wikipedia? Submit your draft for review! |
1
0
0 0
0
0
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0 0
0
0
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0 0
0
0
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Steps:<<<<<<<<<<<>>>>>>>>>>>
Let be a triangle.
The altitudes and intersect at .
We will show that also is perpendicular to , i.e. that it is an altitude of .
• The quadrilateral is cyclic, because .So, also (as angles subtended by the same arc).
• The quadrilateral is cyclic because opposite angles and are supplementary (since ). So, angles and are equal.
• The angles and are equal as vertical angles, i.e. . In the right triangle , we have that , therefore in the triangle it holds that .
We conclude that the three altitudes pass through the same point.