Similar Right Triangles on the same Slope

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 the lengths of their corresponding sides are proportional.

Front

How do you determine if two triangles are similar?

Back

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

Front

What is the significance of slope in relation to similar triangles?

Back

The slope of the sides of similar triangles is the same, which means that the triangles are oriented in the same direction and have the same steepness.

Front

What is the formula for calculating the slope of a line?

Back

The slope (m) of a line is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

If two triangles have the same slope, what can be inferred about their angles?

Back

If two triangles have the same slope, it can be inferred that their corresponding angles are equal, indicating that the triangles are similar.

Front

What does it mean for two lines to be parallel in terms of slope?

Back

Two lines are parallel if they have the same slope, meaning they will never intersect and maintain a constant distance apart.

Front

How can you use proportions to compare the slopes of two lines?

Back

You can set up a proportion using the change in y-values over the change in x-values for both lines and show that they are equal to demonstrate that the slopes are the same.

Front

What is the relationship between the slopes of the hypotenuses of two similar right triangles?

Back

The slopes of the hypotenuses of two similar right triangles are equal, as both triangles share the same angle measures.

Front

What is the importance of integer coordinates in determining slopes?

Back

Using integer coordinates simplifies the calculation of slopes, as the differences in y-values and x-values will also be integers, making it easier to compute and compare slopes.

Front

How can you express the slope of a line using coordinates?

Back

The slope of a line can be expressed as the ratio of the difference in y-coordinates to the difference in x-coordinates of two points on the line.