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9-12 Geometry Unit 7

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K-5 Math 6-8 Math •9-12 Math

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Algebra 1 •Geometry Algebra 2 Extra Support Materials for Algebra 1

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Unit 7

Glossary

Geometry

An arc is a part of a circle’s circumference between two points on the circle.

In this diagram, the blue highlighting shows one arc of the circle.

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A central angle is an angle formed by two radii of a circle that each have an endpoint at the center of the circle.

In this diagram, the angle arc symbol shows one central angle of the circle.

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A chord of a circle is a line segment with both endpoints on the circle.

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The circumcenter of a triangle is the intersection point of all three perpendicular bisectors of the triangle’s sides. It is the center of the triangle’s circumscribed circle.

In this diagram, the circumcenter is point \(D\).

<p>Circle with center D. Triangle ABC inside circle. Dashed lines from D to triangle sides create 90 degree angles. </p>

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When a figure is circumscribed, it is completely surrounded by another figure, so their sides, edges, vertices, or curves touch.

A polygon is circumscribed by a circle if it fits inside the circle and every vertex of the polygon is on the circle.
A circle is circumscribed by a polygon if it fits inside the polygon and every side of the polygon is tangent to the circle.

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If a circle can be drawn around a quadrilateral so that it passes through every vertex, the quadrilateral is called a cyclic quadrilateral.

That is, a cyclic quadrilateral can be circumscribed by a circle.

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The incenter of a triangle is the intersection point of all three of the triangle’s angle bisectors. It is the center of the triangle’s inscribed circle.

In this diagram the incenter is point \(D\).

<p>Triangle A B C with point D in the triangle equidistant from all 3 sides.</p>

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An inscribed angle is an angle formed by two chords of a circle that share an endpoint.

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A radian is a unit of measurement for angles, based on the radius of a circle.

The radian measure of any central angle is this ratio: \(\frac{\text{length of intercepted arc}}{\text{radius}}\)

<p>Circle with radius of 1, arc length l of 1 and central angle measure of 1 radian.</p>

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A sector is the region inside a circle between two radii.

In this diagram, the shaded region shows one sector of the circle.

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A line is tangent to a circle if the line intersects the circle at exactly one point and is perpendicular to the radius.

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Unit 7 Resources

Student Materials