**Identifying Similar Triangles**

This
lesson is a combination geometry/ratio lesson.
Students will have the opportunity to create similar triangles and
discover that when the triangles are changed, the two triangles will continue
to be similar and the ratio of the sides will remain constant. Students will use ** Geometer’s Sketchpad **to
create their triangles. There will be an
expectation that students will already be familiar with the program.

At
the conclusion of the lesson, students will be able to demonstrate
mathematically that they understand how similar triangles have corresponding
sides that maintain a constant ratio and the corresponding angles of the
similar triangles are the same.

Students
will need to be able to determine corresponding sides of triangles and will be
able to use the computer program.

**Assessed QCC: **6^{th} grade Geometry and Spacial
Sense: #16 Topic: Congruence, Similarity Standard:
Identifies congruent and similar geometric figures. #37 Equivalent Representations Standard: Expresses equivalent ratios as a proportion

Gwinnett County AKS
Objectives:** **#31 Identify congruent and similar
geometric figures and #14 Use a ratio to compare two quantities.

**The time duration** for this lesson is 60 minutes.

Students will need paper and
pencil to draw initial similar triangles.

** Geometer’s Sketchpad is** the program that will be used.

**Steps:**

This lesson is taken from ** Geometry
Activities for Middle School Students with the Geometer’s Sketchpad
by** Karen Windham Wyatt,
Ann Lawrence and Gina M. Foletta. The lesson is

Students will already be
familiar with the program.

1.
Construct a
triangle.

2.
Construct a line
that is parallel to one side.

3.
Label all points.

4.
Measure the angles
of the larger triangle and the smaller triangle. Compare.

5.
Measure the sides
of the larger triangle and corresponding smaller triangle’s sides.

6.
Using the
calculator in the program find the ratio of the corresponding sides.

7.
Move the triangle
around and students will note what happens when the
angles change and sides change.

Below is a sample of the
desired drawing for the students.

**Assessment: **After students have created their sketches and
experimented with them, they will print them up and write a paragraph
explaining what they learned about similar triangles.

**Modifications: **This plan will be used for a gifted 6^{th}
grade math class, so there will be no modifications.

**Extensions: **Students might enjoy using this same idea using
similar rectangles or free form polygons.