Similarity of Quadrilaterals
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10) $ABCD \sim DCEF$ $|AB| = 6 \text{cm}$ $|DC| = 10 \text{cm}$ $|EF| = ?$
This question includes visual content: A geometric diagram showing two stacked quadrilaterals: the top one labeled ABCD and the bottom one labeled DCEF. Point D lies on the line segment AF and point C lies on the line segment BE. The text next to the diagram specifies $ABCD \sim DCEF$, with lengths $|AB| = 6$ cm and $|DC| = 10$ cm, asking for the length $|EF|$.
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Hi Metehan, let's solve this geometry problem together. We are given two similar quadrilaterals, which are trapezoids, stacked on top of each other.
Similarity in Trapezoids
The problem states that quadrilateral A B C D is similar to quadrilateral D C E F. This similarity gives us a direct relationship between their corresponding side lengths.
When two figures are similar, the ratios of their corresponding sides are equal. Let's write down the proportions for these two trapezoids.
From the problem, we know that the length of A B is six centimeters and the length of D C is ten centimeters. We are looking for the length of E F.
Using the similarity ratio, we can equate the ratio of the top base to the middle base with the ratio of the middle base to the bottom base.
Note that line segment C D and D C are the same, so C D also has a length of ten centimeters. Let's plug in the known values: six over ten equals ten over E F.
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