Slope and Similar Triangles

Front

What is the definition of slope in a coordinate plane?

Back

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 does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-coordinate increases, the y-coordinate also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-coordinate increases, the y-coordinate decreases, meaning the line falls from left to right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no vertical change regardless of the horizontal change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the horizontal change is 0, leading to division by zero.

Front

How can you determine if two triangles are similar based on their slopes?

Back

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion, which includes having the same slope for corresponding sides.

Front

What is the relationship between the slopes of similar triangles?

Back

The slopes of corresponding sides of similar triangles are equal.

Front

If triangle ABC has a slope of 1, what is the slope of triangle DEF if they are similar?

Back

The slope of triangle DEF is also 1, as similar triangles have equal slopes for corresponding sides.

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.