Montessori Geometry
Circles
In this post, you will find a quick review and free worksheets on: (1) the parts of a circle, (2) the relationship between a circumference and a straight line, and (3) the relationship between two circumferences.
Quick Review: Parts of a Circle
See this interactive presentation of the parts of a circle.
Parts of a circle:
- Center
- Circumference
- Diameter
- Radius
- Arc
- Chord
- Sector
- Segment
- Semicircle
- Tangent
Also refer to this Montessori presentation on the parts of the circle nomenclature.
You can answer the following worksheets online or download the printable version:
Materials
To present the next two lessons, you will need:
- a stick – to represent a straight line
- a hoop or circle – to represent a circumference
Relationship Between a Circumference and a Straight Line
Place a stick and a circle on the table. Move them towards each other but don’t let them touch yet. External. The straight line is external to the circumference.
Move the stick and the circle further towards each other until they are just touching. Tangent. The word tangent comes from the Latin word tangere, meaning to touch. The line is tangent to the circumference — they intersect (or touch) at just one point.
Continue the movements of the stick and circle in the same direction until the stick is on top of the circle. Secant. The line now cuts the circumference at two points. This is called secant, from the Latin secare, meaning to cut.
Relationship Between Two Circumferences
Repeat the process above, but this time with two circles or hoops, one smaller than the other.
When the circles are apart, they are external to each other.
When the smaller circle is just touching but still outside the bigger circle, it is said to be externally tangent.
When the two circles now overlap and touch each other at two points, this is called secant.
When the smaller circle is now inside the bigger circle but still touching it at one point, it is said to be internally tangent.
When the smaller circle is inside the bigger circle but is no longer touching it (no longer tangent), it is said to be internal to the bigger circle.
When the smaller circle is exactly at the center of the bigger circle, both circles are said to be concentric, meaning they have the same point as their center. (Concentric is considered a subset of internal.)
Summary
Remember the following terms:
- external – having no points in common
- tangent – having one point in common
- secant – having two points in common
After working with materials, the worksheets below will help students learn and master these concepts.
Note on the Worksheets
You can reduce the size of the worksheet by zooming out your browser screen. For Windows users, scroll down the mouse wheel while pressing the Ctrl key in your keyboard.
Worksheet 1: Relationship between a circumference and a straight line
liveworksheets.com
Worksheet 2: Relationship between two circumferences
liveworksheets.com
Did you enjoy these worksheets on the relationship between a circumference and a straight line, and the relationship between two circumferences?
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