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    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.

     
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    Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

    Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

     
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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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    Prove the Laws of Sines and Cosines and use them to solve problems.

    Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

     
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    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.

     
    00:00

    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.

     
    00:00

    Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

    Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

     
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    Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied 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