Angle Relationships a Concrete to Abstract Approach. Using GeoLegs to Model Complementary, Supplementary, Linear Pair, and Vertical Angles.

As a geometry student, you have been told about angle relationships, but maybe you haven't grasp the concept behind complementary angles, or supplementary angles. What is a linear pair? What is special and different in a linear pair from just supplementary angles?

In this lesson, we approach the teaching of these concepts making use of the GeoLegs. GeoLegs enable to show in a very concrete way the abstract idea behind those definitions. If you don't have GeoLegs to practice with, it doesn't matter; we make us of high quality pictures and animations that accomplish the same goal. As in other lessons in the geometry section, we offer you the option answer a problem after most of the examples.

Lesson's Content

Lesson's Glossary

Angle
Geometric shape formed by two rays (initial and ending sides of the angle) that share a common endpoint called the vertex. You may name an angle using the vertex, or a point in each ray and the vertex label in the center.

Acute angle
An angle that is between 0 and 90 degrees.

Complement
Angle that together with the given angle adds up to 90 degrees.

Complementary angles
Two angles whose measures, when added together, equal 90 degrees.

Obtuse angle
An angle whose measure is greater than 90 but less than 180 degrees.

Supplement
Angle that together with the given angle adds up to 180 degrees.

Supplementary angles
Two angles whose measures, when added together, equal 180 degrees.

Vertical angles
Nonadjacent angles that are opposite by the vertex and are formed by two intersecting straight lines.

Interactive Geometric Applets: Relevant Theorems.

Drag point C within the shaded area to view different sets of complementary angles.

For this applet drag Point C to generate different sets of supplementary angles.

This applet also illustrates what a linear pair is.

Drag point C, verify how these vertical angles are congruent.

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