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US-VA

Math

Virginia Math

Geometry: Polygons and Circles

Solve problems, using the properties specific to parallelograms, rectangles, rhombi, squares, isosceles trapezoids, and trapezoids.
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Prove and justify that quadrilaterals have specific properties, using coordinate and algebraic methods, such as the slope formula, the distance formula, and the midpoint formula.
Prove and justify theorems and properties of quadrilaterals using deductive reasoning.
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Use congruent segment, congruent angle, angle bisector, perpendicular line, and/or parallel line constructions to verify properties of quadrilaterals.
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Solve problems involving the number of sides of a regular polygon given the measures of the interior and exterior angles of the polygon.
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Justify the relationship between the sum of the measures of the interior and exterior angles of a convex polygon and solve problems involving the sum of the measures of the angles.
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Justify the relationship between the measure of each interior and exterior angle of a regular polygon and solve problems involving the measures of the angles.
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Determine the proportional relationship between the arc length or area of a sector and other parts of a circle.
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Solve for arc measures and angles in a circle formed by central angles.
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Solve for arc measures and angles in a circle involving inscribed angles.
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Calculate the length of an arc of a circle.
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Calculate the area of a sector of a circle.
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Apply arc length or sector area to solve for an unknown measurement of the circle including the radius, diameter, arc measure, central angle, arc length, or sector area.
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Derive the equation of a circle of given the center and radius using the Pythagorean Theorem.
given the coordinates of the endpoints of a diameter of a circle, determine the coordinates of the center of the circle.
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given the coordinates of the endpoints of the diameter of a circle, determine the length of the radius or diameter of the circle.
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given the coordinates of the center and the coordinates of a point on the circle, determine the length of the radius or diameter of the circle; and
given the coordinates of the center and length of the radius of a circle, identify the coordinates of a point(s) on the circle.
a graph of a circle with a center with coordinates that are integers;
coordinates of the center and a point on the circle;
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coordinates of the center and the length of the radius or diameter; and
coordinates of the endpoints of a diameter.
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