Angles of a Triangle: Triangles in the Trees

This is one lesson in a larger Unit Plan that covers many properties of triangles and several other theorems.  It has proofs, real world problems, constructions, a unit project, assessments, and more.  In Lesson 9, “Triangles in the Trees (Angles of a Triangle)”, students investigate the Triangle Sum Theorem, Triangle Inequality Theorem, and Exterior Angle Theorem.  One of the activities is a hands-on activity. Includes lesson plan, and a variety of downloadable student handouts (with and without Geometer's Sketchpad instructions).  The entire unit plan can be found here. The Lesson investigates Triangle Sum Theorem with a hands-on activity. The Triangle Inequality Theorem is discovered through a drawing activity, as is Exterior Angle Theorem. There are also several real world connections.

Standards & Objectives

Academic standards
CLE 3108.4.1
Develop the structures of geometry, such as lines, angles, planes, and planar figures, and explore their properties and relationships.
CLE 3108.4.2
Describe the properties of regular polygons, including comparative classification of them and special points and segments.
GLE 0606.4.1
Understand and use basic properties of triangles, quadrilaterals, and other polygons.
Alignment of this item to academic standards is based on recommendations from content creators, resource curators, and visitors to this website. It is the responsibility of each educator to verify that the materials are appropriate for your content area, aligned to current academic standards, and will be beneficial to your specific students.
Learning objectives: 

Essential Questions:

  • What properties of sides and angles of triangles are used in everyday situations?
  • Why should we study Triangle Sum Theorem, Triangle Inequality Theorem and Exterior Angle Theorem for Triangles?


Lesson Variations

Blooms taxonomy level: 

Helpful Hints


  • Worksheets
  • rulers 
  • compasses
  • protractors
  • computer with internet access