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 Geometerís 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:† 6th 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.
Geometerís Sketchpad †is the program that will be used.
This lesson is taken from Geometry Activities for Middle School Students with the Geometerís Sketchpad †by Karen Windham Wyatt, Ann Lawrence and Gina M. Foletta.† The lesson is Triangle Buddies.†
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 triangleís 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 6th grade math class, so there will be no modifications.
Extensions:†† Students might enjoy using this same idea using similar rectangles or free form polygons.†