# List of Concepts for Algebra and Geometry Placement Tests

Algebra Competency Test:

Before taking the De La Salle “Incoming Frosh Math Placement Test” the student should be able to:

Algebra: 3/2/11

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