1.7

Basic

Constructions

1.7

Basic

Constructions

You will learn how

to construct a

line segment, duplicate an angle, and bisect

a line segment

You will learn how

to construct a

line segment, duplicate an angle, and bisect

a line segment

Construct a segment congruent to a given segment.Given:

A B

Use a straightedge to draw a line.

Construct: A1 B1 = AB

A1

Construction #1Construction #1

Now label the point A1

somewhere on the new line.

Construct a segment congruent to a given segment.Given:

A B

Set your compass for radius AB and make a

mark on the line where B lies. Construct: A1 B1 = AB

A1

Construction #1Construction #1

Then, move your compass to line and set your pointer on A1. Make a mark on the line and label it B1.

A1 B1

l

Construction #2Construction #2Construct a angle congruent to a given angle.

Use a straightedge to draw a ray.

Now make an arc.

Make the same arc on the ray.

Construction #2Construction #2Construct a angle congruent to a given angle.

Make another arc

Repeat the arc.

Connect the endpoint and the intersection

Construction #3Construction #3Bisect a line segment with a perpendicular line.

Make an arc more than half way.

Repeat the arc on the other side.

Connect the intersection

Construction #4Construction #4Bisect an angle with an angle bisector.

Make an arc. Make another arc.

Repeat the arc.

Connect the vertex with the intersection

Assignment

1.7 Basic ConstructionsGeometry

Construct each figure as directed.

1. Construct AB congruent to XY.

2. Construct the perpendicular bisector of XY.

3. Construct the angle bisector of Z.

4. Construct a triangle whose sides are all the same length as XY.

X Y

Z

5. Construct AB so that AB = MN + OP

6. Construct KL so that KL = OP - MN

7. Construct A so that mA = m1 + m2

8. Construct C so that C = 2m2

9. Construct the angle bisector of X

M N O P

1 2

X