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6.10 – Circles and Polygons
No key terms for this section.
- A polygon is a closed plane figure with all straight sides.
- A parallelogram is a quadrilateral with parallel opposite sides
- A rectangle is a parellelogram with all right angles and congruent opposite sides
A square is a rectangle with all congruent sides.
- Inscribed angle – An angle formed by two chords that share an endpoint on a circle.
- It is half the measure of the intercepted arc.
- Supplementary angles – Two angles whose measures have the sum of 180°.
- Complementary angles – Two angles whose measures have the sum of 90°
|Incenters and Circumcenters of Polygons
- The ideas of incenter and circumcenter for all polygons are the same as what you have seen for triangles.
|Inscribed and Circumscribed Circles
- Circle Inscribed in a Polygon
- The circle is inside the polygon and tangent to each side of the polygon.
- Circle Circumscribed About a Polygon
- The circle is wrapped around the outside of the polygon and intersects each of the polygon’s vertices.
- Quadrilaterals inscribed in circles
- The measures of opposite angles of a quadrilateral (4 sided polygon) add up to 180° (supplementary).
- The ONLY parallelogram that can be inscribed in a circle is a rectangle.
- All squares are rectangles.
- Ex 1. In the diagram below, is circumscribed about quadrilateral ABCD. What is the value of x?
- Since opposite angles are supplementary, x + 120 = 180.
- Subtract 120 on both sides: x = 60
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