4.1 Tangent, Slope, and Similar Triangles

Front

What is the equation used to find the value of x in a proportion?

Back

To solve for x in a proportion, you can use the cross-multiplication method, which states that if \( \frac{a}{b} = \frac{c}{d} \), then \( a \cdot d = b \cdot c \).

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning it goes straight up and down and does not have a defined angle of inclination.

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 \( m = \frac{y2 - y1}{x2 - x1} \).

Front

What is the relationship between the sides of similar triangles?

Back

The sides of similar triangles are proportional, meaning the ratios of the lengths of corresponding sides are equal.

Front

What is the formula for the slope of a line segment connecting two points?

Back

The formula for the slope of a line segment connecting two points (x1, y1) and (x2, y2) is \( m = \frac{y2 - y1}{x2 - x1} \).

Front

What is the significance of the slope in real-world applications?

Back

The slope represents the rate of change, which can be used in various real-world applications such as calculating speed, cost per item, or the steepness of a hill.

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 proportional.

Front

How can you determine if two triangles are similar?

Back

Two triangles are similar if their corresponding angles are equal or if the lengths of their corresponding sides are proportional.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating that there is no vertical change as you move along the line.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as it does not have a defined angle of inclination.