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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

STEP 1

1. The problem involves a geometric figure, likely a triangle with segments and points labeled as A,B,C,D,E A, B, C, D, E .
2. The task is to determine which of the given proportions is true based on the geometric configuration.

STEP 2

1. Analyze the geometric configuration.
2. Recall relevant geometric theorems or properties.
3. Evaluate each proportion for truthfulness.

STEP 3

Analyze the geometric configuration:
- Without the image, we assume a common geometric scenario such as a triangle with points D D and E E on sides AB AB and AC AC , respectively. - These points might divide the sides proportionally.

STEP 4

Recall relevant geometric theorems or properties:
- Consider the Basic Proportionality Theorem (also known as Thales' theorem), which states that if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides those two sides proportionally.

STEP 5

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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