## Similar and Congruent Triangles

### Mary Kay BacallaoColleges and Universities - Florida

#### Description

Students create and classify different types of triangles using an online geo-board. They explore the concepts of similar and congruent as they discover how to draw similar and congruent triangles.

#### Objectives

The student draws and classifies two-dimensional figures having up to eight or more sides.

The student knows symmetry, congruency, and reflections in geometric figures using drawings and concrete materials (for example, pattern blocks, mirrors).

The student knows and creates congruent and similar figures.

#### Materials

-A computer with a projector and the Internet
-A computer lab with the Internet or student geo-boards and rubber bands
-Copies of the Similar and Congruent Triangles Quiz (see associated file)
-Math journals

#### Preparations

1. Have the computer connected to the Internet and hooked up to the projector.
2. Have the geo-boards for the students or a computer lab with the Internet.
3. Make copies of the Similar and Congruent Triangles Quiz for the students.

#### Procedures

1. Ask the students, “How can I draw a triangle?” After listening to the student responses, explain the difference between an equilateral and a right triangle and give examples of how to draw them.
2. Go to the Website: http://standards.nctm.org/document/eexamples/chap4/4.2/part2.htm Scroll down to the bottom and then click stand-alone applet.

3. Have the students direct you to draw a triangle on the online geo-board. Click the rubber bands and then click one of the pegs of the geo-board and then another. To make the third side of the triangle, click the middle of one of the line segments and drag it to the third peg. After the triangle is drawn, you can color it in by clicking one of the color squares.

4. Choose another student and draw a second, and then another to draw a third triangle. Continue to draw triangles until you have a variety of triangles such as an isosceles triangle, a right triangle, and an equilateral triangle, if possible. Put the words congruent, similar, isoceles triangle, and right triangle on the board and discuss the meanings of the words. Have the students copy down the words in their journals and write the definitions.

5. Ask the students to describe how the triangles are alike or different. Then teach the students that there are some ways to describe the triangles that we have drawn. Some possibilities include: (1) right triangle, one 90-degree angle (2) isosceles triangle, two equal sides and angles (3) equilateral triangle, all sides equal. We can also draw triangles that do not fit into any of the categories listed above.

6. Clear the geo-board and then focus on one type of triangle, the isosceles triangle. Have the students direct you to draw several isosceles triangles. Discuss the triangles and how they are the same. Then talk about how they are different. Show the students that some are similar, and some are congruent. Yet some are neither similar nor congruent. Clear the board. Draw several congruent triangles by counting pegs over and then up. Draw these congruent triangles in different places and different orientations on the geo-board. Discuss congruency. Clear the board. Draw a small isosceles triangle. Now take the measurement of the base and the measurement of the height and double both of them. Then explain that you are creating another isosceles triangle with the new measurements. It is like the first one in shape, but not in size. Explain this as similar, but not congruent.

7. If the students understand the concepts of similar and congruent, pass out the geo-boards and have them create their own similar and congruent triangles. Have the students work in pairs to practice making similar and congruent triangles. If a computer lab is available, have them explore using the online geo-board. If the students need more explanation, repeat the example in #6 using right triangles.

8. Allow the students to practice and then administer the assessment instrument.

#### Assessments

Use the Similar and Congruent Triangles Quiz in the Associated File as a formative assessment. If the students do not understand the concepts, demonstrate the concepts again on the electronic geoboard by drawing the different types of triangles and having the students identify them. Assist with clues and definitions, then test them again. This lesson only addresses triangles and congruency.

Circulate and formatively assess students as they use the technology tools. Provide assistance for students who are experiencing difficulty and monitor accordingly.

#### Extensions

If a computer lab is available, have the students use the computers with you to explore the concepts of similar and congruent triangles. Have the students work in pairs to practice making similar and congruent triangles before administering the assessment instrument.