Question

definition of slope; $5 - 3 = 15 - 9$; the area of triangle $a$ is greater than the area of triangle $b$; $\frac{5}{3} = $ slope; $\frac{5}{3} = \frac{15}{9}$;

statement \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\treason
drag and drop \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tdrag and drop
an item here \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tan item here
drag and drop \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\ttriangle $a$ is similar to triangle $b$.
an item here

Explanation:

To solve this, we analyze the relationships between the statements and reasons related to triangle similarity and slope (ratios).

Step 1: Identify the statement for "Triangle \( A \) is similar to triangle \( B \)"

For triangles to be similar, their corresponding sides must be proportional (or slopes, if related to linear figures, must be equal). The proportion \( \frac{5}{3} = \frac{15}{9} \) shows proportionality (since \( \frac{15}{9} = \frac{5}{3} \) when simplified). So the statement for the reason "Triangle \( A \) is similar to triangle \( B \)" is \( \boldsymbol{\frac{5}{3} = \frac{15}{9}} \).

Step 2: Verify the proportion

Check \( 5 - 3 = 2 \) and \( 15 - 9 = 6 \) (not equal, so \( 5 - 3 = 15 - 9 \) is false). The proportion \( \frac{5}{3} = \frac{15}{9} \) holds because cross - multiplying gives \( 5\times9 = 45 \) and \( 3\times15 = 45 \), confirming proportionality (a key for triangle similarity).

Answer:

For the "Statement" column (matching the reason "Triangle \( A \) is similar to triangle \( B \)"), the correct item to drag is \( \boldsymbol{\frac{5}{3} = \frac{15}{9}} \).

(If arranging the table:

Statement	Reason