Download Geometry Competency Test - De La Salle High School

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:
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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
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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
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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
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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
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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
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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
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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;
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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
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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
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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
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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