[1-6] Basic Construction

Mr. Joshua DoudtGeometry (H)

September 10, 2015Pg. 42-48

Standard/Objective

• G.CO.12 Make formal geometric constructions with a variety of tools, and methods.

• G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and a distance around a circular arc.

– To make basic constructions using a straight edge and a compass

Activity

In lesson 1-6, you will use a compass to construct geometric figures. You can construct figures to show geometric relationships, to suggest new relationships, or simply to make interesting geometric design.

Get compass and graph paper or blink paper

Activity

Step 1: Open your compass to about 2 in. Make a circle and mark the point at the center of the circle, Keep the opening of you compass fixed. Place compass point on the circle. With the pencil end, make a small arc to intersect the circle.Step 2: Place the compass point on the circle at the arc. Mark another arc. Continue around the circle this way to draw four more arcs – six in all.Step 3: Place your compass point on an arc you marked on the circle. Place the pencil end at the next arc. Draw a large arc that passes through the circle’s center and continues to another point on the circle.Step 4: Draw six large arcs in this manner, each centered at one of the six points marked on the circle, You may choose to color your design.

Discussion

In Step 2, did your sixth mark on the circle land precisely on the point where you first placed your compass on the circle?

Homework: Extend your design by using one of the six points on the circle as the center for a new circle. Repeat steps 1-4 with this circle. Repeat several times to make interlocking circles.

Vocabulary

• Straightedge• Compass• Construction• Perpendicular lines• Perpendicular bisector

Purpose?

You can use special geometric tools to make a figure that is congruent to an original figure without measuring. This method is more accurate than sketching and drawing.

Definition

A straightedge is a rule with no markings on it.

A compass is a geometric tool used to draw circles and parts of circles called arcs.

A construction is a geometric figure drawn using a straight edge and a compass.

Problem 1 – Constructing Congruent Segments

Your turn

Use a straightedge to draw Then construct .

Problem 2 – Constructing Congruent Angles

Your turn

2) a. Construct so that b. How is constructing a congruent angle

similar to constructing a congruent segment.

Compare

• Perpendicular Lines vs. Perpendicular Bisector

Problem 3 – Constructing the perpendicular bisector

Your turn

Draw

Problem 4 – Constructing the Angle Bisector

Your turn

Draw obtuse . Then construct its bisector .