8.4A Slope with Similar Triangles

Front

What is the definition of slope in the context of a graph?

Back

The slope of a line is a measure of its steepness, 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 does it mean for two triangles to be similar?

Back

Two triangles are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.

Front

If triangle HJK is similar to triangle PMK, what can be said about the slopes of lines HK and PK?

Back

The slopes of lines HK and PK are equal because the triangles are similar, meaning the ratios of the change in y-values to the change in x-values are the same.

Front

What is the slope of a line that goes down from left to right?

Back

The slope of a line that goes down from left to right is negative.

Front

What is the slope of a line that goes up from left to right?

Back

The slope of a line that goes up from left to right is positive.

Front

How can you determine if two lines are parallel using their slopes?

Back

Two lines are parallel if they have the same slope.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is zero.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is zero because there is no change in y.

Front

If the coordinates of two points are (1, 2) and (3, 6), what is the slope of the line connecting them?

Back

The slope is m = (6 - 2) / (3 - 1) = 4 / 2 = 2.