Since DE is parallel to AB, and we have a transversal CD, we have alternate interior angles and can conclude that angle CDE is congruent to angle CBA.
Since angle CBA is congruent to angle CDE, we can use the transitive property to say that angle CBA is congruent to angle CDE, which means triangle CDE is congruent to triangle CBA.
Since triangle CBA is congruent to triangle CDE, we can use corresponding parts of congruent triangles to say that CD = BA.
We know that EB = 3 and BA = EB + EA, which means BA = 3 + EA.
We also know that D1 = EA + AC, which means EA = D1 - AC.
Therefore, BA = 3 + D1 - AC.
We can solve for AC by subtracting 5 from CE: AC = CE - 5.
Substituting this into the equation for BA, we get:
BA = 3 + D1 - (CE - 5).
Simplifying, we get: BA = 3 + D1 - CE + 5.
We are given that D1 = 3.8 and CE = 5, so we can substitute these values into the equation to find BA:
BA = 3 + 3.8 - 5 + 5.
Simplifying, BA = 3 + 3.8.
Therefore, BA = 6.8.
Since CD = BA, we can conclude that CD = 6.8.
Therefore, the length of CD is 6.8.
In the diagram below, DE is parallel to AB. CE - 5, D1 = 3.8, and EB = 3. Find the
length of CD. Round your answer to the nearest tenth if necessary.
1 answer