Constructions and Algebra Connections Module 2 Lesson 2

Geometric Construction Geometric construction involves drawing accurate geometric figures without using any measurement. There are different ways of doing geometric constructions, but the oldest, most often used method involves a compass and a straightedge. This is the method we will use in this presentation. A compass is used to draw circles or arcs and a straightedge is used to draw lines. Euclid used this method to discover many geometric concepts that we still study today. He lived over 2000 years ago!

You can use patty paper to construct accurate geometric figures. Patty paper works well because it is translucent (you can see through it) and folds and creases easily. The Geometer’s Sketchpad is but one of many computer applications that you can also use to construct geometric figures.

You will need a compass and straightedge as you work in this assignment.

Constructing a Congruent Angle (copying an angle)

Bisecting an angle by geometric construction.

Bisect a segment: Draw segment AB of any length on your paper.

Move the compass point to the other endpoint.

Angle Bisector

Example 1

Example 2

We successfully solved for x, but that’s not what the question asked!

Carefully check over your work. Make sure your answer is sensible and addresses the question asked!

Your Turn! Give this problem a try. Be sure to draw and label a diagram and to answer the question being asked.

Your work should be similar to this!

Angle Addition This concept is very intuitive. It just makes sense that the measure of the bigger angle in the above diagram is the sum of the measures of the two smaller angles.

Example 1

Example 2

Always be sure to answer the question that is being asked!

Your Turn: Give this one a try before moving to the next slide.

Did you get x = 4? If not try it again before looking at the solution on the next slide?

Here is the solution.

You are now ready to move on to the next assignment in Module 2 Lesson 2.