Data

Copy and paste the text below. It is read-only. Select All

Postulate 1-1 (pg. 12) Through any two points there is exactly one line. Postulate 1-2 (pg. 12) If two lines intersect, then they intersect in exactly one point. Postulate 1-3 (pg. 12) If two planes intersect, then they intersect in exactly one line. Postulate 1-4 (pg. 13) Through any three noncollinear points there is exactly one plane. Ruler Postulate (pg. 25) The points of a line can be put into one-to-one correspondence with the real numbers so that the distance between any two points is absolute value of the difference of the corresponding numbers. Segment Addition Postulate (pg. 26) If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC. Coordinate(s) of a point (pg. 25) Its distance and direction from the origin of a number lines. On a coordinate plane, they are in the form (x,y). Protractor Postulate (pg. 28) Let Ray OA and Ray OB be opposite rays in a plane. Ray OA, ray OB, and all the rays with endpoint O that can be drawn on one side of line AB can be paired with the real numbers from 0 to 180. a. Ray OA is paired with 0 and ray OB is paired with 180. b. If ray OC is paired with x and ray OD is paired with y, then m<COD = Ix - yI. Angle Addition Postulate (pg. 28) If point B is in the interior of <AOC, then m<AOB + m<BOC = m<AOC. If <AOC is a straight angle, then m<AOB + m<BOC = 180. The Distance Formula (Proof on pg. 362, Exercise 46) The distance between (x1, y1) and (x2, y2) is given by: The Midpoint Formula (pg. 45) The coordinates of the midpoint M of line AB with endpoints A(x1,y1) and B(x2,y2) are the following: The Distance Formula (Three Dimensions) (pg.48) The distance between two points (x1,y1,z1) and (x2,y2,z2) can be found using this extension of the Distance Formula: Postulate 1-9 (pg. 54) If two figures are congruent, then their areas are equal. Postulate 1-10 (pg. 54) The area of a region is the sum of the areas of its nonoverlapping parts. Law of Detachment (pg. 83) If a conditional is true and its hypothesis is true, then its conclusion is true. In symbolic form: If p ---} q is a true statement and p is true, the q is true. Law of Syllogism (pg. 83) If p ---} q and q ---} r are true statements, then p ---} r is a true statement. Addition Property Equality (pg. 89) If a = b, then a + c = b + c. Subtraction Property Equality (pg. 89) If a = b, than a - c = b - c. Multiplication Property of Equality (pg. 89) If a = b, then a * c = b * c. Division Property of Equality (pg. 89) If a = b and c 0, then a/c = b/c. Reflexive Property of Equality (pg. 89) a = a Symmetric Property of Equality (pg. 89) If a = b, then b = a. Transitive Property of Equality (pg. 89) If a = b and b = c, then a = c. Substitution Property of Equality (pg. 89) If a = b, then b can replace a in any expression. The Distributive Property (pg. 89) a(b + c) = ab + ac Reflexive Property of Congruence (pg. 91) Line AB =~ Line AB <A =~ <A If A is congruent to B, then B is congruent to A. Symmetric Property of Congruence (pg. 91) If line AB =~ line CD, then line CD =~line AB. If <A =~ <B, then <B =~ <A. Transitive Property of Congruence (pg. 91) If line AB =~ line CD and line CD =~ line EF, then line AB =~ line EF. If <A =~ <B and <B =~ <C, then <A =~ <C. (If A is congruent to B and B is congruent to C, then A is congruent to C.) Vertical Angles Theorem (pg. 98) Vertical angles are congruent. Congruent Supplements Theorem (pg. 99) If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent. Congruent Complements Theorem (pg. 99) If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent. Theorem 2-4 (pg. 99) All right angles are congruent. Theorem 2-5 (pg. 99) If two angles are congruent and supplementary, then each is a right angle. Corresponding Angles Postulate (pg. 116) If a transversal intersects two parallel lines, then corresponding angles are congruent. Alternate Interior Angles Theorem (pg. 116) If a transversal intersects two parallel lines, then alternate interior angles are congruent. Same-side Interior Angles Theorem (pg. 116) If a transversal intersects two parallel lines, then same-side interior angles are supplementary. Converse of the Corresponding Angles Postulate (pg. 122) If two lines and a transversal form corresponding angles that are congruent,then the two lines are parallel. Converse of the Alternate Interior Angles Theorem (pg. 123) If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel. Converse of the Same-Side Interior Angles Theorem (pg. 123) If two lines and a transversal form same-side interior angles that are supplementary, the the two lines are parallel. Theorem 3-5 (pg. 124) If two lines are parallel to the same line, then they are parallel to each other. Theorem 3-6 (pg. 124) In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. Triangle Angle-Sum Theorem (pg. 131) The sum of the measures of the angles of a triangle is 180. m<A + m<B + m<C = 180 Triangle Exterior Angle Theorem (pg. 133) The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles. m<1 = m<2 + m<3 Polygon Angle-Sum Theorem (pg. 145) The sum of the measures of the angles of an n-gon is (n - 2)180. Polygon Exterior Angle-Sum Theorem (pg. 146) The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360. For the pentagon, m<1 + m<2 + m<3 + m<4 + m<5 = 360. Triangle (pg. 144) 3 Quadrilateral (pg. 144) 4 Pentagon (pg. 144) 5 Hexagon (pg. 144) 6 Octagon (pg. 144) 8 Nonagon (pg. 144) 9 Decagon (pg. 144) 10 Dodecagon (pg. 144) 12 n (any number higher) (pg. 144) n-gon Slope-intercept Form (pg. 152) y = mx + b (m is slope; b is y-intercept) Standard Form of a Linear Equation (pg. 153) Ax + By = C Point-slope Form (pg. 154) y - y1 = m( x -x1) Finding Slope (pg. 154) m = y2 - y1 / x2 - x1 Slope of Parallel Lines (pg. 158) If two nonvertical lines are parallel, their slopes are equal. If the slopes of two distinct nonvertical lines are equal, the lines are parallel. Any two vertical lines are parallel. Slopes of Perpendicular Lines (pg. 159) If two nonvertical lines are perpendicular, the product of the slopes if -1. If the slopes of two line has a product of -1, the lines are perpendicular. Any horizontal line and vertical line are perpendicular. 3rd Angle Theorem (pg. 181) If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent. Side-Side-Side (SSS) Postulate (pg. 187) If the three sides of one triangle are congruent to the three sides of another triangle, the the two triangles are congruent. Side-Angle-Side (SAS) Postulate (pg. 188) If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. Angle-Side-Angle (ASA) Postulate (pg. 195) If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. Angle-Angle-Side (AAS) Theorem (pg. 195) If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent. CPCTC (pg. 203) Once you have triangles congruent, you can make conclusions about their other parts because, by definition, corresponding parts of congruent triangles are congruent. Legs (pg. 211) If two sides are congruent in a triangle... Base (pg. 211) The third side of the triangle other than the legs. Vertex Angle (pg. 211) Between the legs. Base Angles (pg. 211) The other two angles located near the base. Isosceles Triangle Theorem (pg. 211) If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Converse of Isosceles Triangle Theorem (pg. 211) If two angles of a triangle are congruent, then the sides opposite the angles are congruent. Theorem 4-5 (pg. 211) The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. Corollary (pg. 212) A statement that follows immediately from a theorem. Corollary to Isosceles Triangle Theorem (pg. 212) If a triangle is equilateral, then the triangle is equiangular. Corollary to Converse of Isosceles Triangle Theorem (pg. 212) If a triangle is equilateral, then the triangle is equilateral. Hypotenuse (pg. 217) In a right triangle, the side opposite of the right angle and the longest side. Hypotenuse-Leg (HL) Theorem (pg. 217) If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another triangle, then the right triangles are congruent. Convex Polygon (pg. 144) Has no diagonal with points outside the polygon Concave Polygon (pg. 144) Has a least one diagonal with points outside the polygon Flow Proof (pg. 123) Arrows show the logical connections between the statements Two-Column Proof (pg. 117) The statements and reasons are aligned in columns. Alternate Interior Angles (pg. 115) Nonadjacent interior angles that lie on opposite sides of the transversal. Same-Side Interior Angles (pg. 115) Lie on the same side of the transversal t and between l and m. Corresponding Angles (pg. 115) Lie on the same side of the transversal t and in corresponding positions in relative to l and m. Paragraph Proof (pg. 98) Written as sentences in a paragraph