(Motivate) The perpendicular from the center of a circle to a chord bisects the chord and conversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord.ģ. (Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse.Ģ. (Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and in half of it and (motivate) its converse.ġ. (Motivate) In a parallelogram, the diagonals bisect each other and conversely.Ħ. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.ĥ. (Motivate) In a parallelogram opposite angles are equal, and conversely.Ĥ. (Motivate) In a parallelogram opposite sides are equal, and conversely.ģ. (Prove) The diagonal divides a parallelogram into two congruent triangles.Ģ. (Motivate) The sides opposite to equal angles of a triangle are equal.ġ. (Prove) The angles opposite to equal sides of a triangle are equal.Ħ. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).Ĥ. Recall of algebraic expressions and identities. Factorization of ax2 + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem. ![]() Statement and proof of the Factor Theorem. Motivate and State the Remainder Theorem with examples. Constant, linear, quadratic and cubic polynomials. Coefficients of a polynomial, terms of a polynomial and zero polynomial. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws.)ĭefinition of a polynomial in one variable, with examples and counter examples. ![]() Recall of laws of exponents with integral powers. Rationalization (with precise meaning) of real numbers of the type 1/(a+b√x) and 1/( √x + √y) (and their combinations) where x and y are natural number and a and b are integers.ĥ. Definition of nth root of a real number.Ĥ. If two lines intersect, then they intersect in exactly one point (Theorem 1).3. If a point lies outside a line, then exactly one plane contains both the line and the point (Theorem 2). If two lines intersect, then exactly one plane contains both lines (Theorem 3). ![]() If two planes intersect, then their intersection is a line (Postulate 6).Ī line contains at least two points (Postulate 1). If two points lie in a plane, then the line joining them lies in that plane (Postulate 5). Through any two points, there is exactly one line (Postulate 3). Through any three noncollinear points, there is exactly one plane (Postulate 4). Theorem 3: If two lines intersect, then exactly one plane contains both lines.Įxample 1: State the postulate or theorem you would use to justify the statement made about each figure.įigure 1 Illustrations of Postulates 1–6 and Theorems 1–3.Theorem 2: If a point lies outside a line, then exactly one plane contains both the line and the point.Theorem 1: If two lines intersect, then they intersect in exactly one point.Postulate 6: If two planes intersect, then their intersection is a line.Postulate 5: If two points lie in a plane, then the line joining them lies in that plane.Postulate 4: Through any three noncollinear points, there is exactly one plane.Postulate 3: Through any two points, there is exactly one line.Postulate 2: A plane contains at least three noncollinear points. ![]() Postulate 1: A line contains at least two points.Listed below are six postulates and the theorems that can be proven from these postulates. A theorem is a true statement that can be proven. Summary of Coordinate Geometry FormulasĪ postulate is a statement that is assumed true without proof.Slopes: Parallel and Perpendicular Lines.Similar Triangles: Perimeters and Areas.Proportional Parts of Similar Triangles.Formulas: Perimeter, Circumference, Area.Proving that Figures Are Parallelograms.Triangle Inequalities: Sides and Angles.Special Features of Isosceles Triangles.Classifying Triangles by Sides or Angles.Lines: Intersecting, Perpendicular, Parallel.
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