Question

part g
write a fraction setting the vertical length of the larger triangle over its horizontal length. what does this fraction represent?

space used(includes formatting): 0 / 30000

part h
write a fraction setting the vertical length of the smaller triangle over its horizontal length. what does this fraction represent?

space used(includes formatting): 0 / 30000

part i
to see if the slopes are the same, write an equation setting the two fractions equal to each other. is this equation true? why or why not? what does that mean about the slope between points e and a and the slope between the points a and c?

Explanation:

To solve these parts, we need to assume some values for the vertical and horizontal lengths of the triangles (since the diagram is not provided, we'll use a general approach). Let's assume:

Part G

Let the vertical length of the larger triangle be \( V_L \) and the horizontal length be \( H_L \). The fraction is \( \frac{V_L}{H_L} \). This fraction represents the slope of the line forming the larger triangle (or the slope between two points, e.g., E and A or A and C depending on the diagram).

Part H

Let the vertical length of the smaller triangle be \( V_S \) and the horizontal length be \( H_S \). The fraction is \( \frac{V_S}{H_S} \). This fraction represents the slope of the line forming the smaller triangle (the same line as the larger triangle if they are similar or on the same line).

Part I

The equation setting the two fractions equal is \( \frac{V_L}{H_L} = \frac{V_S}{H_S} \). If the triangles are similar (or on the same straight line), this equation is true because the slope of a line is constant. This means the slope between points E and A and the slope between points A and C are equal, indicating a straight line (constant slope).

Final Answers (assuming typical values, e.g., larger triangle: vertical = 6, horizontal = 4; smaller triangle: vertical = 3, horizontal = 2)

• Part G: Fraction: \( \frac{6}{4} \) (simplifies to \( \frac{3}{2} \)), represents the slope of the line.
• Part H: Fraction: \( \frac{3}{2} \), represents the slope of the line.
• Part I: Equation: \( \frac{6}{4} = \frac{3}{2} \) (simplifies to \( \frac{3}{2} = \frac{3}{2} \)), which is true. This means the slope between E and A and A and C is the same (constant slope, straight line).

Answer:

To solve these parts, we need to assume some values for the vertical and horizontal lengths of the triangles (since the diagram is not provided, we'll use a general approach). Let's assume:

Part G

Let the vertical length of the larger triangle be \( V_L \) and the horizontal length be \( H_L \). The fraction is \( \frac{V_L}{H_L} \). This fraction represents the slope of the line forming the larger triangle (or the slope between two points, e.g., E and A or A and C depending on the diagram).

Part H

Let the vertical length of the smaller triangle be \( V_S \) and the horizontal length be \( H_S \). The fraction is \( \frac{V_S}{H_S} \). This fraction represents the slope of the line forming the smaller triangle (the same line as the larger triangle if they are similar or on the same line).

Part I

The equation setting the two fractions equal is \( \frac{V_L}{H_L} = \frac{V_S}{H_S} \). If the triangles are similar (or on the same straight line), this equation is true because the slope of a line is constant. This means the slope between points E and A and the slope between points A and C are equal, indicating a straight line (constant slope).

Final Answers (assuming typical values, e.g., larger triangle: vertical = 6, horizontal = 4; smaller triangle: vertical = 3, horizontal = 2)

• Part G: Fraction: \( \frac{6}{4} \) (simplifies to \( \frac{3}{2} \)), represents the slope of the line.
• Part H: Fraction: \( \frac{3}{2} \), represents the slope of the line.
• Part I: Equation: \( \frac{6}{4} = \frac{3}{2} \) (simplifies to \( \frac{3}{2} = \frac{3}{2} \)), which is true. This means the slope between E and A and A and C is the same (constant slope, straight line).