Lesson objective: Understand that when given three side lengths of a triangle, the sum of the lengths of two sides must be greater than the length of the third side in order for the triangle to form.

Students bring prior knowledge of triangles that can be categorized based on their angle types from 4.G.A.1. This prior knowledge is extended to looking at the lengths of the sides of the triangle and attempting to draw the triangle. Students conclude that as long as the sum of the lengths of two sides of a triangle is greater than the length of the third side, a triangle will form. A conceptual challenge students may encounter is that some students think that any three side lengths will form a triangle.

The concept is developed through work with a diagram, which asks students to consider the lengths of three sides of a triangle and determine if those sides could be used to form a triangle.

This work helps students deepen their understanding of equivalence because students will look at inequality statements to determine if the side lengths can form a triangle.

Students engage in Mathematical Practice #5 (use math tools strategically) as they draw triangles that have the side lengths they are considering.

**Key vocabulary:**

- acute triangle
- angle
- base angle
- isosceles triangle
- obtuse triangle
- right triangle
- side
- Triangle Inequality Theorem
- vertex

**Special materials needed:**