Answered

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*prove de/ae = bd/ce*
triangle proportionality.
i am able to find that the triangles are similar but don’t know how to prove the parallel sides are proportional to the side segments

Prove Deae Bdce Triangle Proportionality I Am Able To Find That The Triangles Are Similar But Dont Know How To Prove The Parallel Sides Are Proportional To The class=

Sagot :

sqdancefan

Explanation:

You can use the definition of similarity to show that corresponding sides are proportional. You cannot prove anything about the proportionality of non-corresponding sides.

Statement . . . . Reason

1. BD║CE . . . . given

2. ∠A≅∠A . . . . reflexive property of congruence

3. ∠ABD≅∠ACE . . . . corresponding angles theorem

4. ΔABD ~ ΔACE . . . . AA similarity postulate

5. BD/CE = AD/AE . . . . definition of similarity

_____

Additional comment

Length DE is related to BC in the same way that AD is related to AB. There is no way to prove the ratio you show in your problem statement. You can show that ...

  DE/AE = (CE -BD)/CE = 1 -(BD/CE) . . . . the difference is proportional to the corresponding longer side

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