Up

Perpendicular segment constructions

Constructions are an important part of geometry. Architects, interior designers as well as other professions that need accurate drawings use them. You will need a ruler and a compass.

 

Perpendicular bisectors are a particularly important construction. An example of where they can be used in real life would be to determine the best possible spot to place a cell phone tower so that the three surrounding towns all receive the same level of service.

 

A perpendicular bisector is a line that divides another line into two equal parts at a right angle.

 

Here are the steps to constructing a perpendicular bisector of a line.

 

  1. Set the width of the compass to a little more than half of the total line (the width doesn’t matter so much, as long as it does not change during this step)
  2. Put the point of the compass on one endpoint of the line and use the pencil side to draw a small arc on the top and the bottom of the line.
  3. Without changing the width, repeat this step using the other endpoint of the line.
  4. The arcs should intersect at a point above and a point below the line. Using the ruler, connect these points with a straight line. This is your perpendicular bisector.

 

Perpendicular bisectors can be used together to create properties that would help with situations similar to the above example of the cell phone tower. The spot where all three perpendicular bisectors of a triangle intersect is called the circumcenter. A circumcenter is equidistant (or of equal distance) to all three vertices, or corners, of a triangle.

 

Here are the steps to constructing a circumcenter of a triangle.

 

  1. Repeat the above steps and construct the perpendicular bisector of one of the sides of the triangle.
  2. Do this again for a different side.
  3. You can construct the third perpendicular bisector for added accuracy, but you only need two to find the circumcenter.
  4. The circumcenter is the spot where the perpendicular bisectors intersect. It can be inside the triangle, outside the triangle, or right on one of the sides of the triangle.

 

This point in the triangle is called the circumcenter because if you were to circumscribe a circle around the triangle, the circumcenter would be the center of this circle. To circumscribe is when you draw a figure around another enclosing it while connecting all the points.

 

Here are the steps to circumscribing a circle around a triangle.

 

  1. Repeat the steps of finding the circumcenter.
  2. Place the point of the compass on the circumcenter and the pencil side on one of the vertices of the triangle.
Carefully, use the compass to draw a circle around the triangle. The circle should enclose the whole triangle while connecting all three vertices.

Downloads:
1315 x

Construct the perpendicular bisector of each.

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

Example of one question:

Constructions-Perpendicular-segment-constructions-Easy

Watch below how to solve this example:

 

Downloads:
902 x

Locate the circumcenter of each triangle.

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

Example of one question:

Constructions-Perpendicular-segment-constructions-Medium

Watch below how to solve this example:

 

Downloads:
820 x

Circumscribe a circle about each triangle.

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

Example of one question:

Constructions-Perpendicular-segment-constructions-Hard

Watch below how to solve this example:

 
 
 

Facebook PageGoogle PlusTwitterYouTube 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