In the illustration(in the link below) , suppose that DE ∥ BC. Find DE. (Assume BC = 10.)
DE = ?
www.webassign.net/ewenmath10/12-4-001-alt.gif
Because of the possible problems involved, we do not go to links.
To find the length of DE in the given illustration, we can use the concept of similar triangles. Since DE is parallel to BC, it forms a pair of corresponding angles with BC.
Here are the steps to solve the problem:
1. Observe that the triangles ABE and CDE are similar because they have the same corresponding angles:
∠ABE = ∠CDE (corresponding angles)
∠AEB = ∠CED (alternate interior angles)
∠BAE = ∠DCE (corresponding angles)
2. Hence, we can set up a proportion to find the length of DE in terms of the given information:
AB / CD = AE / CE
3. Substitute the known values into the proportion:
AB / 10 = 6 / CE
4. Rearrange the proportion to isolate CE:
CE = (10 * 6) / AB
5. Since AB and CE are corresponding sides of similar triangles, they are proportional to each other. Therefore, we can set up another proportion using the given information:
AB / DE = AE / CE
6. Substitute the known values into the proportion:
10 / DE = 8 / CE
7. Substitute the value of CE from step 4 into the above proportion:
10 / DE = 8 / (10 * 6 / AB)
8. Simplify and solve for DE:
DE = (10 * AB) / (8 * 6)
9. Finally, substitute the value of AB (which is not given) to get the exact length of DE.