Triangle Properties and Line Segments

This video tutorial explains how to write equations for the median, right bisector, and altitude of a triangle. It begins with definitions and then provides step-by-step examples using triangle ABC and triangle DEF. The tutorial covers calculating slopes, midpoints, and y-intercepts to form equations in the format y = mx + b.

What is a median in a triangle?

• A line that divides the triangle into two equal areas

• A line that is parallel to one side of the triangle

• A line that bisects an angle

• A line segment from a vertex to the midpoint of the opposite side

What is the equation of a line in the form y = mx + b used for?

• Finding the length of a line segment

• Describing the relationship between x and y coordinates on a line

• Calculating the area of a triangle

• Determining the angle between two lines

How do you find the midpoint of a line segment?

• By dividing the x and y coordinates of the endpoints

• By multiplying the x and y coordinates of the endpoints

• By subtracting the x and y coordinates of the endpoints

• By averaging the x and y coordinates of the endpoints

In Example 1, what is the first step to find the median from vertex C?

• Calculate the midpoint of the opposite side

• Find the slope of the line

• Draw the triangle

• Determine the y-intercept

What is a right bisector?

• A line that divides the triangle into two equal areas

• A line that intersects a line segment at its midpoint at a 90-degree angle

• A line that divides an angle into two equal parts

• A line that is parallel to one side of the triangle

In Example 1, how is the slope of the right bisector of AB determined?

• By using the negative reciprocal of the slope of AB

• By averaging the slopes of the triangle's sides

• By using the same slope as AB

• By calculating the angle between AB and the x-axis

What is an altitude in a triangle?

• A line that divides the triangle into two equal areas

• A line segment from a vertex that forms a 90-degree angle with the opposite side

• A line that is parallel to one side of the triangle

• A line that bisects an angle

In Example 1, what is the slope of the altitude from vertex C?

• The slope of the line connecting the midpoints of the triangle

• The average of the slopes of the triangle's sides

• The same as the slope of the opposite side

• The negative reciprocal of the slope of the opposite side

In Example 2, what is the first step to find the median from vertex E?

• Calculate the midpoint of the opposite side

• Find the slope of the line

• Determine the y-intercept

• Draw the triangle

In Example 2, how is the slope of the right bisector of DF determined?

• By averaging the slopes of the triangle's sides

• By using the same slope as DF

• By using the negative reciprocal of the slope of DF

• By calculating the angle between DF and the x-axis