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# Triangle Construction Site

Lesson 1 of 11

## Objective: Students will be able to understand why it is possible to prove that two triangles are congruent without knowing the measures of all sides and angles. Students will be able to determine whether it is possible to construct more than one triangle given a set of side and angle measurements.

In this section, students use an interactive online simulation to identify sets of conditions that guarantee triangles congruence (**MP5**).

Ideally, every student should have their own computer, although two students could complete the activity by sharing one computer. The activity is based on the NCTM Illuminations Triangle Congruence Resource, found on the Internet.

Before students log in to the computers, I have them complete parts 1-3 of the activity (*TriangleConstructionSite_Activity.docx*). The goal is for students to list all possible combinations of three sides or angles of a given measure, and then to make conjectures about which ones can only be assembled into a single triangle. Students also are asked to examine combinations that might be duplicates, considering that triangles which are rotations or reflections of one another are congruent. This should take about 5 minutes. I want students to make these conjectures themselves, but if necessary, I will show students how to proceed by using an LCD projector to display my computer screen while I demonstrate.

Once students have made conjectures, they list all the combinations of elements that they will investigate in the table provided in the handout (part 4). They then log in to the computers, go to the URL of the Triangle Congruence Resource, and begin testing their conjectures. I use a handout here to structure students’ approach to the activity: first make conjectures, then compare

observations with predictions.

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#### Lesson Close + Homework

*5 min*

I display the lesson close question on the front board using the slideshow. I have the students brainstorm in pairs, then in teams, before writing their answers in their learning journals. The purpose of the learning journal is to encourage students to reflect on what they have learned (as well as to provide individual accountability). Since this activity will be conducted in the computer lab, I do not have one student from each team to write a team answer on the white board.

Before class is dismissed, I remind students of their homework assignment, textbook problems 5-50, 5-68, 5-70, as are listed on the unit syllabus.

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- UNIT 1: Models and Constructions
- UNIT 2: Dimension and Structure
- UNIT 3: Congruence and Rigid Motions
- UNIT 4: Triangles and Congruence
- UNIT 5: Area Relationships
- UNIT 6: Scaling Up- Dilations, Similarity and Proportional Relationships
- UNIT 7: Introduction to Trigonometry
- UNIT 8: Volume of Cones, Pyramids, and Spheres

- LESSON 1: Triangle Construction Site
- LESSON 2: Proving Triangles Congruent
- LESSON 3: Introduction to Two-Column Proof
- LESSON 4: Applying Triangle Congruence
- LESSON 5: Progress Check and Homework Review 1
- LESSON 6: Reasoning About Constructions
- LESSON 7: Verifying Properties of Constructions
- LESSON 8: Proving Properties of Quadrilaterals 1
- LESSON 9: Proving Properties of Quadrilaterals 2
- LESSON 10: Progress Check and Homework Review 2
- LESSON 11: Triangle Congruence Unit Quiz