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    Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

    Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.

    Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

     
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    Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

    Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

     
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    Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. (side side side, side angle side, angle side angle)nt.HSG-CO.B.8, CCSS.Math.Content.HSG-CO.B.7

     
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    Construct a tangent line from a point outside a given circle to the circle.

    Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

     
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    Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

    Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments.

     
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    G-CO.10
    Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

     
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    Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

     
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    Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

     
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    Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

     
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    Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.