Geometric Constructions: Congruent Segments and

Congruent Angles

GeometryMr. ZampettiUnit 2, Day 1

5 Types of Constructions

• Congruent Segments• Congruent Angles• Perpendicular Bisectors • Angle Bisectors• Parallel Lines

Needed Materials:

• Compass (an instrument for drawing or describing circles, measuring distances, etc., consisting generally of two movable, rigid legs hinged to each other at one end)

• Straight Edge

Constructing Congruent Segments

• You will be given a segment that looks similar to this:

A B

Constructing Congruent Segments

• Step 1: Draw a reference line with your straightedge upon which you will make your construction

• Step 2: Place a starting point on the reference line (A’)

• Step 3: Place the point of the compass on Point A

Constructing Congruent Segments

• Step 4: Stretch the compass so that the pencil is exactly on Point B.

• Step 5: Without changing the span of the compass, place the compass point on A’ and swing the pencil so that it crosses the reference line.  Label that B’

Watch the video!

Regentsprep.org

Now practice…

Constructing Congruent Angles

• You will be given an angle that looks similar to this:

B

A C

Constructing Congruent Angles

• Step 1: Draw a reference line with your straightedge upon which you will make your construction

• Step 2: Place a starting point on the reference line (A’)

• Step 3: Place the point of the compass on the vertex (Point A)

Construction Congruent Angles

• Step 4: Stretch the compass to any length so long as it stays ON the angle

• Step 5: Swing an arc with the pencil that crosses both sides of BAC

• Step 6: Without changing the span of the compass, place the compass point on A’ and swing an arc that will intersect the reference line and go above the reference line.

Construction Congruent Angles• Step 7: Go back to BAC and measure

the width of where the arc crosses the rays that form the angle

• Step 8: With this width, place the compass point on the reference line where your new arc crosses and mark off this width on your new arc.

• Step 9: Connect this new intersection point to the starting point on the reference line.

Watch the video!

Regentsprep.org

Now practice…