To prove: The length of corresponding diagonals are in the same ratio to the length of corresponding sides.
Explanation of Solution
Given information:
Below quadrilaterals are similar.
Consider two similar quadrilaterals as shown below.
Since the above two quadrilaterals are similar, it implies that the corresponding sides are in the same ratio and also the corresponding
Also, it follows that,
It is required to prove that the lengths of the corresponding diagonals are in the same ratio as the length of the corresponding sides.
In view of (1), it is sufficient to show that,
Note that in
This implies that
Since the corresponding sides in a similar triangles are proportional.
This implies that,
That is, The length of corresponding diagonals are in the same ratio to the length of corresponding sides.
The ratio of other two diagonals
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McDougal Littell Jurgensen Geometry: Student Edition Geometry
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