# Activities

• • • ##### Subject Area

• Math: Geometry: Triangles

• ##### Author 6-8

60 Minutes

• ##### Device
• TI-73 Explorer™
• ##### Other Materials
This is Activity 3 from the EXPLORATIONS Book:
Shaping Middle Grades Mathematics: Activities for Geoboard and the TI-73

## Move Along Little Vertex

#### Activity Overview

In this activity, students use the Geoboard to determine the area of triangles having the same base and same height.

#### Before the Activity

• Start the Geoboard App and format it
• See the attached PDF file for detailed instructions for this activity
• Print pages 21 - 31 from the attached PDF file for your class
• #### During the Activity

Distribute the page to the class.

• Construct two parallel line segments
• Between these two parallel lines build three different triangles, each with the same base and same height
• Use the calculator to find and record the area of each triangle
• Observe they have the same area
• Note that moving a vertex of a triangle along a line that is parallel to the triangle's base does not change the triangle's height nor its area
• Observe that shifting a triangle's vertex between parallel lines can change any triangle into a right triangle with the same area

• Draw a diagonal and redesign the quadrilateral using triangles between parallel lines
• Calculate the area of the triangle formed and thus the area of the quadrilateral

• Using triangles between parallel lines move one vertex so that a pentagon changes to a quadrilateral with the same area

• Solve word problems to measure area of geometric figures using triangles between parallel lines
• #### After the Activity

Students complete the Activity sheet and answer questions.

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary