Lesson Designed By:

Maureen Capuzzi
Montville High School, NJ
(201) 540-9002

Edited by:

Janet Mae Zahumeny
Roselle Park High School
e-mail: 74620.2745@compuserve.com

TOPIC:

Given the Rim of a Plate, Find It's Age

LEVEL:

Secondary Plane Geometry

GEOMETER'S SKETCHPAD PROFICIENCY:

Beginner / Intermediate

CLASS TIME:

1 class period (42 minutes)

GEOMETER'S SKETCHPAD SKILLS NEEDED:

Students should be familiar with the CONSTRUCT and MEASURE menus.

NOTES TO TEACHER:

To begin this activity students should be familiar with the terms : circle, center, arc, chord, perpendicular and bisect, or have access to a dictionary or geometry book.

INVESTIGATION: Given the Rim of a Plate, Find It's Age

Construction of a circle, given an arc of the circle.

SITUATION:

Archaeologists have unearthed a piece of a rim of a plate. There are no marks which would indicate the age of the plate. They do know that plates with diameters greater than 28 cm. are representative of an era before 300 BC. If the diameter is less than or equal to 28 cm, then the plate had to have been made in the year 300 BC or later. (Plates made before 300 BC are worth a lot more money!)

PROBLEM:

Given the piece of the rim of the plate, find the age of the plate.

PROCEDURE:

1 Construct any 2 chords of the given circle.

2. Construct midpoints of the 2 chords.

3. Construct perpendiculars to the chords through their midpoints.

4. Label the points of intersection of the perpendicular bisectors.

5. Measure the distance from the point of intersection to center of the circle.

6. Double this distance to find the diameter of the plate.

7. Re-read the problem and prepare a statement which will advise the archaeologists if
they are "in the money"

The figure below shows how their final sketch should appear.