Education Technology

# Activities

• ##### Subject Area

• Math: Geometry: Triangles

9-12

60 Minutes

• ##### Device
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition
• ##### Software

Cabri Geometry™
TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
This is Activity 5 from the EXPLORATIONS Book:
Exploring The Basics Of Geometry With Cabri

Bisectors

#### Activity Overview

Students investigate the Perpendicular Bisector Theorem and examine its converse. They also explore the Angle Bisector Theorem.

#### Before the Activity

Install the Cabri™: Jr. App on the students' graphing calculators using one of these two methods:

• TI-Connect™,  a TI Connectivity Cable, and the Unit-to-Unit Link Cable
• TI-Navigator™  "send to class" feature
• See the attached PDF file for detailed instructions for this activity
• Print pages 17 - 21 from the attached PDF file for your class
• #### During the Activity

Distribute the pages to the class.

• Draw a segment AB and construct its perpendicular bisector
• Label the point of intersection of segment AB and the perpendicular bisector as C
• Construct point D on the perpendicular bisector
• Measure and record the lengths of AD and BD
• Drag point D along the line and measure the lengths of AD and BD
• Observe that the lengths od AD and BD remain equal for any position of point D
• Observe that any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment
• Identify that the triangle formed by points A, B, and D is an isosceles triangle

• Construct a segment AB
• Measure the length of segment AB
• With the same measure, create a segment AC
• Connect points B and C to form an isosceles triangle
• Move the vertex A and observe that point A is equidistant from point B and point C
• Construct a perpendicular bisector of segment BC
• Observe that point A lies on the perpendicular bisector of segment BC
• Drag point A along the perpendicular bisector to verify the observation that a point which is equidistant from the endpoints of a segment, lies on its perpendicular bisector

• Draw an angle and construct its angle bisector
• Construct a point on the bisector in the interior of the angle
• Measure the distance from this point to the rays of the angle
• Identify that the distance from the point to each ray is equal
• Drag the point along the bisector to verify this observation
• Understand that a point that lies on the angle bisector of an angle, is equidistant from the sides of the angle
• #### After the Activity

Review student results:

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