Similar Triangles and Slope

Front

What is the definition of slope?

Back

The slope of a line is a measure of its steepness, 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 it mean for triangles to be similar?

Back

Triangles are similar if they have the same shape but may differ in size. This means their corresponding angles are equal and their corresponding sides are in proportion.

Front

If a line has a slope of 3/2, what does this indicate about its steepness?

Back

A slope of 3/2 indicates that for every 2 units of horizontal change, the line rises 3 units vertically, making it relatively steep.

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 involves division by zero (no horizontal change).

Front

How can you determine if two lines are parallel using their slopes?

Back

Two lines are parallel if they have the same slope.

Front

How can you determine if two lines are perpendicular using their slopes?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

If a line passes through the points (1, 2) and (3, 6), what is its slope?

Back

Using the slope formula, m = (6 - 2) / (3 - 1) = 4 / 2 = 2.