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Theorem. The diagonals of a rectangle bisect each other and have the same length.

Theorem. The diagonals of a rectangle bisect each other and have the same length.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Theorem. The diagonals of a rectangle bisect each other and have the same length. Proof. Let DABCD be a rectangle, i.e., a quadrilateral that has insert defin- ing characteristic. Draw diagonals AC and BD. insert figure that illustrates the setup Explain why the diagonals bisect each other. (Do not work too hard. Make use of a combination of theorems we have already proven.) Next we will show the diagonals have the same length. Note that AC is a side of triangle blah and BD is a side of triangle blah. Thus it suffices to show triangles blah and blah are congruent because then their corresponding sides will be congruent. insert figure highlighting the two triangles of interest Write an argument for why the triangles you identified in the previous step are congruent. insert a diagram that uses color or line style to mark the segments or angles you are using to justify congruence of the triangles Therefore the corresponding sides AC and BD are congruent. Thus the diagonals of a rectangle bisect each other and have the same length.
Transcribed Image Text:Theorem. The diagonals of a rectangle bisect each other and have the same length. Proof. Let DABCD be a rectangle, i.e., a quadrilateral that has insert defin- ing characteristic. Draw diagonals AC and BD. insert figure that illustrates the setup Explain why the diagonals bisect each other. (Do not work too hard. Make use of a combination of theorems we have already proven.) Next we will show the diagonals have the same length. Note that AC is a side of triangle blah and BD is a side of triangle blah. Thus it suffices to show triangles blah and blah are congruent because then their corresponding sides will be congruent. insert figure highlighting the two triangles of interest Write an argument for why the triangles you identified in the previous step are congruent. insert a diagram that uses color or line style to mark the segments or angles you are using to justify congruence of the triangles Therefore the corresponding sides AC and BD are congruent. Thus the diagonals of a rectangle bisect each other and have the same length.
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