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GEOMETRY DISTRICT COURSE PROFICIENCIES The student will be able to: use the terms equidistant, point, line, and plane. use the terms collinear, coplanar, and intersection. find distances. use postulates and theorems relating points, lines, and planes. apply the definitions of complementary and supplementary angles. apply the definition and theorems about perpendicular lines. plan proofs and then write them in two-column form. state and apply the theorem about the intersection of two parallel planes by a third plane. classify triangles according to sides and to angles. apply the theorem about the measure of an exterior angle of a triangle. identify the corresponding parts of congruent figures. deduce information about segments and angles after proving that two triangles are congruent. use AAS theorem to prove triangles congruent. prove that two overlapping triangles are congruent. apply the theorem about a point on the perpendicular bisector of a segment. prove that certain quadrilaterals are parallelograms. apply the midpoint theorem for triangles. determine whether a parallelogram is a rectangle, square, or rhombus. use the exterior angle inequality theorem. solve for an unknown term in a given proportion. use the AA similarity postulate to prove triangles similar. use the SAS and SSS similarity theorems to prove triangles similar. determine the geometric mean between two numbers. determine the lengths of two sides of a 45-45-90 or a 30-60-90 triangles. recognize inscribed polygons and circumscribed circles. draw representations of points, lines, and planes. use symbols for lines, segments, rays, and distances. name angles and their measures. use the midpoint theorem and the angle bisector theorem. state and use the theorem about vertical angles. state and apply the theorems about angles, supplementary to, or complementary to congruent angles. distinguish between intersecting lines, parallel. lines, and skew lines. identify the angles formed when two lines are cut by a transversal. apply the theorem and the corollaries about the sum of the measures of the angles of a triangle. find the measures of interior angles and exterior angles of convex polygons. prove two triangles congruent by using the SSS postulate, SAS postulate. apply the theorems and corollaries about isosceles triangles. use the HL theorem to prove that two right triangles are congruent. apply the definitions of the median and the altitude of a triangle and the perpendicular bisector of a segment. apply the definition of a parallelogram and the theorems about the properties of a parallelogram. apply theorems bout parallel lines. identify the special properties of a rectangle, rhombus, and a square. apply the definitions and identify the properties of a trapezoid and an isosceles trapezoid. apply the inequality theorems and corollaries for one triangle. apply the properties of similar polygons. use similar triangles to deduce information about segments or angles. apply the triangle proportionality theorem. apply the Pythagorean theorem. solve right triangle problems by using the tangent ratio. apply theorems that related tangents and radii. recognize circumscribed polygons and inscribed circles. apply theorems about the chords of a circle. solve problems involving lengths of chords, secant segments, and tangent segments. use the formulas for area to find the area of a regular polygon and sectors of a circle. apply properties of arcs and central angles. solve problems and prove statements involving inscribed angles and angles formed by chords, secants, and tangents. use formulas for perimeter and area of parallelograms, rectangles, triangles, rhombuses, and trapezoids. use the formulas for volume to find the volume of cones, cylinders and total areas of cones and cylinders.