Basic Constructions

I. Copy a segment

II. Copy an angle

What is a Construction?

• Uses TWO instruments only– Compass– Straightedge

• Since a compass measures the radius of a circle, and radii of a circle are congruent, then we can use it to construct congruent segments.

• A straightedge is used to connect two points. A ruler may not be used to measure distances in constructions.

• Definition:– An arc is any part of a circle.

What is a Construction?

–When we draw using a compass we will be drawing arcs. We rarely need to complete the entire circle. The radii will still be congruent even if a complete circle is not present.

Construction #1: Copy a Segment

Given , construct a segment congruent to on line l.AB AB

AB

CD

Step 1: Use the straightedge to draw a line and label it l

Step 2: Choose any point on l and label it C.

Step 3: Set the compass at A and make an arc at B.

Step 4: Using the same opening, set your compass at C and make an identical arc so that it intersects line l. Label this point D.

l

Put compass point here

Put compass point here

AB CD

Step 2: Opening your compass to any comfortable distance, set the compass at C and make an arc that intersects both sides of the angle. Label these points E and D.Step 3: Using the same opening, set the compass at F and make an identical arc which intersects the line l. Label this point G.

Construction #2: Copy an Angle

CD

E

G

Step 1: You need to start with a line l and a point F which corresponds to C.

Step 4: On the original angle, set the compass at D and make an arc that intersects the other side of the angle at E.

Put compass point here

Put compass point here

Put compass point here

F

l

CD

E

H

F G

Construction #2: Copy an AngleStep 5: Using the same opening, set your compass at G and make an identical arc so that it intersects the arc from step 3. Label this point H.

Step 6: Draw FH��������������

ECD HFG

Put compass point here