Question

determine whether each statement can be assumed from the figure.
text alternative
euler lane
gauss lane
fermat street
euclid street
descartes drive
can be assumed
cannot be assumed
euler lane and fermat street intersect.
euler lane and gauss lane are parallel.
fermat street is perpendicular to descartes drive.
gauss lane intersects euclid street between euler lane and descartes drive.
the distance from euclid street to fermat street is the same whether you take euler lane or gauss lane

Explanation:

To determine whether each statement can be assumed from the figure, we analyze each one:

1. Euler Lane and Fermat Street intersect

• In a plane, two lines (Euler Lane is a lane, Fermat Street is a street—both are lines) that are not parallel will intersect. From the figure, they appear to be non - parallel, so their intersection can be assumed. So the answer for this statement is "Can Be Assumed".

2. Euler Lane and Gauss Lane are parallel

• Visually, Euler Lane and Gauss Lane have the same slope (they don't converge or diverge), so we can assume they are parallel. So the answer for this statement is "Can Be Assumed".

3. Fermat Street is perpendicular to Descartes Drive

• There is a right - angle symbol (implied by the figure's drawing) between Fermat Street and Descartes Drive, so we can assume they are perpendicular. So the answer for this statement is "Can Be Assumed".

4. Gauss Lane intersects Euclid Street between Euler Lane and Descartes Drive

• Gauss Lane is a line that crosses Euclid Street, and from the figure, the intersection point is between Euler Lane and Descartes Drive. So we can assume this. So the answer for this statement is "Can Be Assumed".

5. The distance from Euclid Street to Fermat Street is the same whether you take Euler Lane or Gauss Lane

• Since Euler Lane and Gauss Lane are parallel (from statement 2), the distance between two parallel lines (Euclid Street and Fermat Street, with Euler and Gauss as transversals) is constant. So the distance along either transversal (Euler Lane or Gauss Lane) between Euclid and Fermat Street should be the same. So we can assume this. So the answer for this statement is "Can Be Assumed".

For each statement:

1. Euler Lane and Fermat Street intersect: Can Be Assumed
2. Euler Lane and Gauss Lane are parallel: Can Be Assumed
3. Fermat Street is perpendicular to Descartes Drive: Can Be Assumed
4. Gauss Lane intersects Euclid Street between Euler Lane and Descartes Drive: Can Be Assumed
5. The distance from Euclid Street to Fermat Street is the same whether you take Euler Lane or Gauss Lane: Can Be Assumed

Answer:

To determine whether each statement can be assumed from the figure, we analyze each one:

1. Euler Lane and Fermat Street intersect

• In a plane, two lines (Euler Lane is a lane, Fermat Street is a street—both are lines) that are not parallel will intersect. From the figure, they appear to be non - parallel, so their intersection can be assumed. So the answer for this statement is "Can Be Assumed".

2. Euler Lane and Gauss Lane are parallel

• Visually, Euler Lane and Gauss Lane have the same slope (they don't converge or diverge), so we can assume they are parallel. So the answer for this statement is "Can Be Assumed".

3. Fermat Street is perpendicular to Descartes Drive

• There is a right - angle symbol (implied by the figure's drawing) between Fermat Street and Descartes Drive, so we can assume they are perpendicular. So the answer for this statement is "Can Be Assumed".

4. Gauss Lane intersects Euclid Street between Euler Lane and Descartes Drive

• Gauss Lane is a line that crosses Euclid Street, and from the figure, the intersection point is between Euler Lane and Descartes Drive. So we can assume this. So the answer for this statement is "Can Be Assumed".

5. The distance from Euclid Street to Fermat Street is the same whether you take Euler Lane or Gauss Lane

• Since Euler Lane and Gauss Lane are parallel (from statement 2), the distance between two parallel lines (Euclid Street and Fermat Street, with Euler and Gauss as transversals) is constant. So the distance along either transversal (Euler Lane or Gauss Lane) between Euclid and Fermat Street should be the same. So we can assume this. So the answer for this statement is "Can Be Assumed".

For each statement:

1. Euler Lane and Fermat Street intersect: Can Be Assumed
2. Euler Lane and Gauss Lane are parallel: Can Be Assumed
3. Fermat Street is perpendicular to Descartes Drive: Can Be Assumed
4. Gauss Lane intersects Euclid Street between Euler Lane and Descartes Drive: Can Be Assumed
5. The distance from Euclid Street to Fermat Street is the same whether you take Euler Lane or Gauss Lane: Can Be Assumed