Up

Medians

In Geoemetry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposing side.

properties-of-triangles-medians-1

In the figure above, the medians are in red.  Notice that each median bisects one side of the triangle, so that the two lengths on either side of the median are equal.

Example:

Find \(x\) if \(CY = \frac{1}{2}x - 1\) and \(CZ = \frac{{2x - 9}}{2}\)

properties-of-triangles-medians-2

Solution:  Here the median \(XC\) bisects the length \(ZY\), so that each of the two segments \(CZ\) and \(CY\) are equal to each other.  Since \(CZ = CY\), we have

\(\frac{1}{2}x - 1 = \frac{{2x - 9}}{2}\)

Multiplying both sides by 2 gives us


\(x - 2 = 2x - 9\)

Then solving for \(x\), we have

\(x = 7\)

So you see that the median can be useful for solving triangle problems.


Example:  Find \(x\) if \(FS = x\) and \(FY = x + 3\)

properties-of-triangles-medians-3

Solution:  Here the median \(FY\) passes through the centroid of the triangle.  By the property of the centroid, this will cut the median \(FY\) into two segments \(FS\) and \(SY\) whose lengths are in the ratio 2:1. That is, if \(FS = x\), we have that \(SY = \frac{1}{2}x\). Then the sum of \(FS\) and \(SY\) is \(FY\). That is,


\(x + \frac{1}{2}x = x + 3\)

Then by multiplying both sides by 2, we have


\(2x + x = 2x + 6\)

and solving for \(x\) gives us \(x = 6\).




Downloads:
5483 x

Each figure shows a triangle with one or more of its medians.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Properties-of-Triangles-Medians-Easy

Watch below how to solve this example:

 

Downloads:
5010 x

Each figure shows a triangle with one or more of its medians.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Properties-of-Triangles-Medians-Medium

Watch below how to solve this example:

 

Downloads:
4136 x

Each figure shows a triangle with one or more of its medians.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Properties-of-Triangles-Medians-Hard

Watch below how to solve this example:

 
 
 

Facebook PageYouTube Channel

Algebra and Pre-Algebra

Beginning Algebra
Adding and subtracting integer numbers
Dividing integer numbers
Multiplying integer numbers
Sets of numbers
Order of operations
The Distributive Property
Verbal expressions
Beginning Trigonometry
Finding angles
Finding missing sides of triangles
Finding sine, cosine, tangent
Equations
Absolute value equations
Distance, rate, time word problems
Mixture word problems
Work word problems
One step equations
Multi step equations
Exponents
Graphing exponential functions
Operations and scientific notation
Properties of exponents
Writing scientific notation
Factoring
By grouping
Common factor only
Special cases
Linear Equations and Inequalities
Plotting points
Slope
Graphing absolute value equations
Percents
Percent of change
Markup, discount, and tax
Polynomials
Adding and subtracting
Dividing
Multiplying
Naming
Quadratic Functions
Completing the square by finding the constant
Graphing
Solving equations by completing the square
Solving equations by factoring
Solving equations by taking square roots
Solving equations with The Quadratic Formula
Understanding the discriminant
Inequalities
Absolute value inequalities
Graphing Single Variable Inequalities
Radical Expressions
Adding and subtracting
Dividing
Equations
Multiplying
Simplifying single radicals
The Distance Formula
The Midpoint Formula
Rational Expressions
Adding and subtracting
Equations
Multiplying and dividing
Simplifying and excluded values
Systems of Equations and Inequalities
Graphing systems of inequalities
Solving by elimination
Solving by graphing
Solving by substitution
Word problems