# High School: Introduction to Geometry Proofs

Subjects:

Common Core, Math

9, 10, 11

## Goal

Students will discuss knowledge and research about triangles and prove a theorem about triangles.

## Objective

Students will understand what a theorem is and how theorems are used in math.

Students will prove one theorem about triangles.

## Materials

Computers and materials for research (consider setting up a Google search with web sites that you want students to use)

Large chart paper

## Do Now: Journal Entry and Discussion (5 minutes)

Ask students to write silently for two minutes and then discuss: How do you know something is true in math?

## Research (20 minutes)

Tell students that in geometry, mathematicians create theorems, or statements that are proven based on previous theorems and ideas. In geometry, we write proofs to use knowledge and concepts to prove theorems. We are going to start our study of geometry proofs with the study of triangles.

Divide students into groups to use Internet and other resources to research triangles. Have students research the questions: What do we know about triangles? What is always true about triangles? Provide students with 15 minutes to research. Students should cite their sources and references for each piece of information that they find.

## Research Review and Synthesis (10 minutes)

As a whole group, compile the information that you found. In addition, compile a list of web sites that provide good references for math.

## Guided Practice (15 minutes)

Based on the information that students find. Create a geometry proof for a core triangle concept or problem (for example, prove the Pythagorean theorem or prove the area of a triangle).

## Math Talk (5 minutes)

Ask students to revisit their journal entry from the beginning of class and add to their answer. Then, as a class, discuss:

Why is it important to prove what we know in math?

How does the organization of a proof help communicate ideas?