8.4A Slope with Similar Triangles

Front

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

Back

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

Front

How do you calculate the slope of a line given 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 they have the same shape but not necessarily the same size, meaning their corresponding angles are equal and their corresponding sides are in proportion.

Front

If triangle ABC has a slope of -1/2, what does this indicate about its orientation?

Back

A slope of -1/2 indicates that for every 2 units moved horizontally to the right, the line moves down 1 unit, showing a downward slope.

Front

What is the relationship between the slopes of similar triangles?

Back

The slopes of similar triangles are equal, meaning that if two triangles are similar, their corresponding sides will have the same slope.

Front

How can you determine the slope of a line from a graph?

Back

To determine the slope from a graph, select two points on the line, calculate the rise (change in y) and run (change in x), and then use the slope formula: slope = rise/run.

Front

What is the slope of a line that goes through the points (3, 4) and (7, 2)?

Back

Using the slope formula, the slope is calculated as: m = (2 - 4) / (7 - 3) = -2/4 = -1/2.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates a horizontal line, meaning there is no vertical change as you move along the line.

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates a vertical line, where the x-coordinates are the same, resulting in a division by zero in the slope formula.

Front

If triangle DEF has a slope of 3, what can be said about triangle GHI if it is similar to triangle DEF?

Back

If triangle GHI is similar to triangle DEF, then triangle GHI also has a slope of 3.