La Habra High School
Mathematics Department

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Integrated Geometry Standards

GEOMETRIC PRINCIPLES

• recognize differences between inductive and deductive reasoning.
• develop proofs involving geometric figures.
• write two-column, paragraph, and/or flow proofs.
• distinguish between valid and invalid arguments.
• apply rules of logic to an argument.
• prove & apply that triangles are congruent or similar using their corresponding parts.
• extend the concept of similarity to right triangles.
• develop properties of congruence and similarity.
• apply the theorems and converses of parallel lines cut by a transversal.
• determine the properties of each quadrilateral.
• find perimeter, circumference, area, volume, and lateral & surface area of geometric figures.
• calculate volumes & surface areas of cylinders, spheres, prisms, cones, & pyramids.
• analyze the effect of changing dimensions on the surface area and volume.
• classify triangles and quadrilaterals.
• find side lengths and angle measures of triangles and quadrilaterals.
• use angle properties to find missing measurements in triangles and quadrilaterals.
• determine distance and find missing lengths of sides of right triangles using the Pythagorean Theorem.
• use midpoint, distance, and slope formulas to prove the properties of triangles and quadrilaterals.
• find the side or angle of a right triangle using trigonometric ratios.
• transform geometric figures in the coordinate plane.

INTRODUCTORY ALGEBRAIC PRINCIPLES

• apply the rules of positive, negative, and rational exponents.
• convert word problems into linear equations &/or inequalities and solve.
• represent linear equations &/or linear inequalities on a Cartesian plane.
• determine the x- and y- intercepts algebraically and graphically.
• use substitution to verify the location of a point with respect to the line.
• write an equation given two points.
• determine the slope of a line parallel or perpendicular to a given line.
• write an equation of a line through a given point that is parallel or perpendicular to a given line.
• evaluate the solution set of two linear equations or two linear inequalities.
• graph the solution set or estimate the solution from a graph.
• factor second and simple third degree polynomials.
• recognize patterns to factor quadratics.
• use factoring to solve a quadratic equation.
• recognize the difference between a relation and a function.
• identify functions using the vertical line test.
• determine whether a function is increasing or decreasing.
• identify the domain and range of a function.
• recognize the quadratic formula and when to use it.
• use the quadratic formula to find the roots of an equation.
• graph a quadratic function.
• identify the x-intercepts as the solution of a quadratic function.
• determine the number of real solutions of a given quadratic function.
• identify the hypothesis and conclusion in logical deduction.
• use counterexamples to refute an argument or an assertion.

INTERMEDIATE ALGEBRAIC PRINCIPLES

• solve equations by using substitution, graphing, matrices, and addition.
• compute the discriminant to find if the solutions are real or complex.
• evaluate and simplify complex expressions.
• simplify rational expressions.
• solve quadratic equations.
• derive the quadratic formula algebraically.
• determine how the graph of a parabola changes as a, b, and c vary.
• find the maximum, minimum, and zeros of the function.
• know and apply the laws of exponents.
• use these functions in problems involving exponential growth and decay.
• determine the difference between permutation and combination problems.
• apply the permutation and combination formulas to find the probability of an event.
• use Pascal's Triangle to compute probabilities.
• expand expressions using the Binomial Theorem.
• simplify rational expressions by factoring.
• apply rational operations to mixture problems.
• use properties of the number system to prove or disprove statements.
• use properties of numbers to construct valid arguments.

LINEAR ALGEBRA, PROBABILITY & STATISTICS

• compute sums, differences, and products of matrices in real-life situations.
• simplify a matrix expression.
• identify the number and type of solutions in linear systems.
• interpret graphical representation of the linear system.
• solve systems of linear equations using matrices and their inverses.
• identify when and why matrices have inverses.
• solve for probabilities of particular events in finite sample spaces.
• find probabilities of binomial experiments.
• apply the probabilities of binomial experiments to different real-life situations.