6th Grade Math Textbook, Fundamentals

 &KDSWHU

9-10

Triangle Constructions

Objective To construct a triangle congruent to a given triangle• To construct a

triangle given three line segments

Meg’s task is to create a triangle congruent to triangle GHIwithout using
a protractor and ruler. Can Meg use a construction to accomplish this task?

To decide if a construction can be used for this task,
review what you know about geometric constructions.

As you have seen in earlier lessons,

are drawings made with a compass and a straightedge.

• To create lengths, arcs, and circles, you use a compass.


• To draw line segments or sides, you use a straightedge.


• It is important to label your constructions correctly. Use tick marks
  and angle marks to show congruence of corresponding sides and angles.

Use compass and straightedge to construct a triangle that is congruent to GHI.

geometric constructions

Using your straightedge, draw a line.

Draw and label a point Aon the line.

Open your compass to the length of GH.

With your compass on point A, draw an

arc above AB.

A

AB

Open your compass to the length ofGI.

With the compass on point A, draw an

arc that intersects the line. Label the point

of intersection as point B.

Open your compass to the length of HI.

With your compass on point B, draw an arc

above AB. Label the intersection of the

two arcs as point C.

AB

C

AB

AB  GI

GI

H

Using your straightedge, draw ACand CB.

Because each pair of corresponding sides are congruent,

triangle ACB is congruent to triangle GHI. So a construction can

be used to create congruent triangles without protractor or ruler.

ACBGHI

AB

C

AC  GH CB  HI