Question

1. multiselect which statement is true about the graph? select all that apply. (lesson 3)

the ratio of the rise to the run of each triangle is the same.
the smaller triangle and the larger triangle shown are similar.
the slope of the line is 2.
the slope of the line is -2.
the corresponding sides of the two triangles are not proportional.

Explanation:

Step1: Analyze slope triangles

For similar triangles (formed by the line and grid), the ratio of rise to run (slope) is constant. The line has a negative slope (decreasing from left to right).

Step2: Check each statement

• "The ratio of the rise to the run of each triangle is the same." True, as slope is constant for a line.
• "The smaller triangle and the larger triangle shown are similar." True, same slope means corresponding angles equal (AA similarity).
• "The slope of the line is 2." False, line is decreasing, slope negative.
• "The slope of the line is -2." True, e.g., if run = 1, rise = -2 (or vice versa for triangle ratios).
• "The corresponding sides of the two triangles are not proportional." False, similar triangles have proportional sides.

Answer:

• The ratio of the rise to the run of each triangle is the same.
• The smaller triangle and the larger triangle shown are similar.
• The slope of the line is -2.