SWBAT describe the properties of isosceles triangles

Students will use Geometer's Sketchpad to discover properties of isosceles triangles, which they will use to create a graphic organizer and to write proofs.

6 minutes

As students walk in the room, I hand them a computer and instruct them to sign on to Geometer’s Sketchpad. In a previous lesson, students investigated the properties of the medians and mid-segments of triangles. In this lesson, students continue their investigations about properties of triangles. For the Do Now, students work on the following:

- Construct segment AB.
- Construct the perpendicular bisector of segment AB. Label the midpoint of “M.”
- Construct point C on the perpendicular bisector of segment AB.
- Connect point C to points A and B.

While the students work, I walk around the room and check that their triangles "pass the drag test." I drag the vertices and lines to make sure the students have constructed the midpoint and perpendicular bisector of segment AB and not just places points and lines that appear to be the midpoint and perpendicular bisector.

8 minutes

To begin the Mini-Lesson, we go over the question, “What type of triangle have you formed?" Students measure segments AC and BC in order to prove the triangle is isosceles.

We then fold three pieces of different colored paper into a Six-Tab Graphic Organizer, which is based on one of Dinah Zike’s foldables. Rather than writing notes directly in their notebooks, I have students use this graphic organizer. The different colors of the papers and the manipulative aspect help students remember the concepts written on their graphic organizer. They will write down the properties of an isosceles triangle later in the lesson.

After students create their graphic organizer, they copy the information from the Smartboard presentation on the front of their organizers and fill in the first tab based on the information investigated in the beginning of the Mini-Lesson. For example, on the first tab, students write the definition of an isosceles triangle, “An isosceles triangle is a triangle with two congruent sides.”

**Teacher's Technology Note**: If you click on the different tabs of the graphic organizer in the Smart Notebook file, the remaining information students need to write will be shown.

23 minutes

At the beginning of the activity, I hand out a worksheet and assign pairs of students a property to investigate using Geometer’s Sketchpad. The investigations correspond to questions from the worksheet.

- Question 2 refers to the base angles of the triangle
- Question 3 refers to the median as a segment bisector
- Question 4 refers to the median as an angle bisector
- Question 5 refers to the median as an altitude

Students perform their investigation and answer the corresponding question. As they work, I circulate around the room and help clarify questions and address any misconceptions. If students finish their assigned question, they can continue working on the other questions.

After about 8 minutes, each pair shares out what they have found to the class. Since more than one pair will be working on a question, the different pairs can critique the responses. As students are presenting, the other students in the class fill in the information in their graphic organizers.

8 minutes

As a summary, students fill in the last tab of their graphic organizer, triangle ACM is congruent to triangle BCM. They write a formal or informal proof showing why the two triangles are congruent. This leads into a lesson where students will write proofs about the properties of isosceles triangles.

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