Slope Triangles

Front

What is the definition of 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

How do you determine the slope of a line?

Back

The slope of a line is determined by the ratio of the rise (the vertical change) to the run (the horizontal change) between two points on the line.

Front

What is the formula for calculating slope?

Back

The formula for calculating slope is \( \text{slope} = \frac{rise}{run} \) or \( m = \frac{y_2 - y_1}{x_2 - x_1} \).

Front

What does a positive slope indicate about a line?

Back

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

Front

What is the significance of the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle, and is crucial for calculating the slope in slope triangles.

Front

How can you visually represent slope using triangles?

Back

You can visually represent slope using right triangles, where the vertical leg represents the rise and the horizontal leg represents the run.

Front

What is the relationship between the slopes of similar triangles?

Back

The slopes of similar triangles are equal, as they have the same angle measures and proportional side lengths.

Front

What is the rise in the context of slope triangles?

Back

The rise refers to the vertical change between two points on a line, indicating how much the line goes up or down.

Front

What is the run in the context of slope triangles?

Back

The run refers to the horizontal change between two points on a line, indicating how much the line goes left or right.