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Transcript
Geometry Competency Test: Please note that students taking the Geometry Competency Test must also take an Algebra Competency Test at DLS to determine appropriate placement (Date and Time for this test TBA). Before taking the De La Salle “Incoming Frosh Geometry Competency Test” the student should be able to: Sketch simple figures of the basic terms in geometry and their intersections Recognize and analyze a conditional statement Write or verbalize conditional statements to describe properties of points, lines, and planes Recognize and use definitions and biconditional statements Write the converse, inverse, and contrapositive of conditional statements; Apply the properties of equality from algebra Justify statements about congruent segments Justify statements about congruent angles. Supply reasons for statements in a proof Prove properties about special pairs of angles Identify relationships between lines Identify angles formed by transversals Apply theorems about perpendicular lines Prove and use properties of parallel lines; Prove and use theorems to prove that lines are parallel Use slopes of lines to identify parallel and perpendicular lines in the coordinate plane Write equations of lines in the coordinate plane Classify triangles by sides and by angles Find angle measures in triangles Identify congruent figures and corresponding parts Prove triangles are congruent Apply congruence postulates in real-life problems Use congruent triangles to plan and write proofs Use congruent triangles to prove constructions are valid Apply properties of isosceles, equilateral, and right triangles Place geometric figures in a coordinate plane Write coordinate proofs Apply properties of perpendicular bisectors of the sides of triangles Apply properties of angle bisectors of triangles Apply properties of medians of a triangle Apply properties of altitudes of a triangle Locate, by construction, the incenter, circumcenter, centroid, and orthocenter Identify the midsegments of a triangle and use the midsegment theorem Apply the properties of midsegments both logically and algebraically Identify, name, and describe polygons Find the measure of the interior angles of a polygon Apply the definition and theorems about a parallelogram Prove that quadrilaterals are or are not parallelograms Apply the definitions and theorems about rectangles, rhombuses, and squares Apply the definitions and theorems about trapezoids and kites Prove and use the properties of the diagonals of parallelograms, trapezoids, and kites Determine, by formal and/or coordinate proof, if a quadrilateral is a special type Derive and use formulas to find the area of quadrilaterals Identify similar polygons Apply properties of similar polygons to solve problems Identify similar triangles Prove triangles similar by using the AA Similarity Postulate, the SAS Similarity Theorem, and the SSS Similarity Theorem Use the similarity of triangles to deduce information about segments and angles Use proportionality theorems to calculate segment lengths Divide a segment into a given number of equal parts by construction Identify dilations Find the geometric mean between two numbers; Apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle Prove the Pythagorean theorem by formal proof and by algebraic methods; Find lengths using the Pythagorean theorem Determine if a triangle is a right, obtuse, or acute by using the converse of the Pythagorean theorem Find the lengths of the sides of the special triangles when one length is given Solve right triangles and real-life problems by using trigonometry; Define: sphere, circle, radius, chord, diameter, tangent, secant, chord, concentric circles Construct circumscribed and inscribed polygons and circles Apply theorems that relate tangents and radii Apply properties of arcs and central angles; Apply theorems about chords, secants, and tangents of a circle Write the equation of a circle Use the equation of a circle and its graph to solve problems Find the measure of interior and exterior angles of polygons Derive and apply formulas for the area of an equilateral triangle and for regular; polygons Draw a regular polygon and find its center, radius, apothem, and central angle Derive formulas for area and circumference of a circle by relating them to the area and perimeter of a regular polygon; Compute the areas and circumferences of circles Compute arc lengths and areas of sectors of circles. Apply the relationships between scale factors, perimeters and areas of similar figures Use properties of polyhedra to find the number of faces, edges, sides, or to find the measure of angles Calculate the lateral area and total area of right prisms, right cylinders, right pyramids, and right cones Find the volume of prisms, cylinders, cones, and pyramids Find the area and volume of a sphere Apply the properties of similar solids Locate images of figures by reflection, translation, glide reflection, and rotation Identify and use reflections, rotations, translations, and glide reflections Represent transformations as compositions of simpler transformations Geometry: 3/2/11