Similar Triangles and Slope

Front

What are similar triangles?

Back

Similar triangles are triangles that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

What is the definition of slope?

Back

Slope is a measure of the steepness of a line, typically represented 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 line that rises 3 units for every 2 units it runs?

Back

Front

Back

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 it would involve division by zero (no horizontal change).

Front

How can you determine if two triangles are similar using their angles?

Back

If two triangles have two corresponding angles that are equal, then the triangles are similar by the Angle-Angle (AA) similarity criterion.

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope, meaning they never intersect and maintain a constant distance apart.

Front

What is the relationship between the slopes of perpendicular lines?

Back

The slopes of perpendicular lines are negative reciprocals of each other. If one line has a slope of m, the other will have a slope of -1/m.