Slope and Similar Triangles

Front

What is the definition of slope in mathematics?

Back

The slope is a measure of the steepness or incline of a line, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

If a line rises from left to right, what can you say about its slope?

Back

The slope is positive.

Front

If a line falls from left to right, what can you say about its slope?

Back

The slope is negative.

Front

What does a slope of 1 indicate about a line?

Back

A slope of 1 indicates that for every unit the line rises, it also runs one unit horizontally, creating a 45-degree angle with the x-axis.

Front

What is the relationship between similar triangles and slope?

Back

Similar triangles have the same slope because their corresponding sides are proportional.

Front

If triangle ABC is similar to triangle DEF, what can be said about their slopes?

Back

The slopes of corresponding sides of triangles ABC and DEF are equal.

Front

What is the slope of line AC if the rise is 3 and the run is 1?

Back

The slope of line AC is 3 (slope = rise/run = 3/1).