Math  /  Geometry

QuestionGiven the image, which proportion is true? ADAB=AEAC\frac{A D}{A B}=\frac{A E}{A C} ACAE=ABDB\frac{A C}{A E}=\frac{A B}{D B} AEEC=ABDB\frac{A E}{E C}=\frac{A B}{D B} DBAD=AEπC\frac{D B}{A D}=\frac{A E}{\pi C}

Studdy Solution
Evaluate each proportion for truthfulness:
- ADAB=AEAC\frac{A D}{A B}=\frac{A E}{A C}: This proportion is true if DE DE is parallel to BC BC by the Basic Proportionality Theorem. - ACAE=ABDB\frac{A C}{A E}=\frac{A B}{D B}: This proportion does not generally hold without additional conditions. - AEEC=ABDB\frac{A E}{E C}=\frac{A B}{D B}: This proportion is true if DE DE is parallel to BC BC , by the Converse of the Basic Proportionality Theorem. - DBAD=AEπC\frac{D B}{A D}=\frac{A E}{\pi C}: This proportion is not standard and seems to involve a typographical error with πC\pi C.
The true proportion, assuming DE DE is parallel to BC BC , is:
ADAB=AEAC \boxed{\frac{A D}{A B}=\frac{A E}{A C}}

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