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VOCABULARY LIST TERM DEFINITION SEMESTER1 LESSON 6 : SOME FAMOUS THEOREMS OF GEOMETRY Pythagorean Theorem The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. Angle Sum Theorem The sum of the angles of a triangle is 180º. Two Circle Theorems 1. If the diameter of a circle is d, its circumference is πd. 2. If the radius of a circle is r, its area is πr2 . LESSON 5 : COMPLEMENTARY AND SUPPLEMENTARY ANGLES Complementary Angles Two angles are complementary iff their sum is 90º. Supplementary Angles Two angles are supplementary iff their sum is 180º. Theorem 3 Complements of the same angle are equal. Theorem 4 Supplements of the same angle are equal. LESSON 6 : LINEAR PAIRS AND VERTICAL ANGLES Opposite Rays Rays that point in opposite directions Linear Pair Two angles are a linear pair iff they have a common side and their other sides are opposite rays. Vertical Angles Two angles are vertical angles iff the side of one angle are opposite rays to the sides of the other. Theorem 5 The angles in a linear pair are supplementary Theorem 6 Vertical angles are equal. LESSON 7 : PERPENDICULAR AND PARALLEL LINES Perpendicular Two lines are perpendicular iff they form a right angle. Parallel Two lines are parallel iff the lie in the same plane and do not intersect. Theorem 7 Perpendicular lines form four right angles. Theorem 8 If the angles in a linear pair are equal, then their sides are perpendicular. LESSON 3 : PROTRACTOR AND ANGLE MEASURE Degree The oldest unit of measurement. One degree is equal to 1 out of 360. A full set of degrees (360) makes a full rotation of rays. Half/180 is a half rotation of rays. Coordinate Every ray corresponds to exactly one real number called its coordinate. Every real number from 0 to 180 i has exactly one coordinate or ray. Protractor Postulate The rays in a half rotation can be numbered from 0 to 180 so that positive number differences measure angles. Angle An angle is Acute iff it is less than 90º Right iff it is 90º Obtuse iff it is more than 90º but less than 180º Straight iff it is 180º Betweenness of Rays A ray is between two others in the same half rotation iff its coordinate is between their coordinates. LESSON 4 : BISECTION Midpoint of a Line Segment A point is the midpoint of a line segment iff it divides the line segment into two equal segments. Bisect A line bisections an angle iff it divides the angle into two equal angles. Congruent “Coinciding exactly when superimposed.” Corollary A theorem that can easily be proved as a consequence of a postulate or another theorem. Corollary to Ruler Postulate A line segment has exactly one midpoint. Corollary:Protractor Postulate An angle has exactly one ray that bisects it CHAPTER 4, LESSON 1 : COORDINATES AND DISTANCE 1D Coordinate System Locating a coordinate on a line. 2D Coordinate System Locating a coordinate in a plane. Two coordinates locate a point on the plane, using the 2D coordinate system. Usually in grid form. X-Axis The horizontal axis: perpendicular to y-axis. Y-Axis The vertical axis: perpendicular to x-axis. Distance Formula The distance between the points P1 (x1, y1) and P2 (x2, y2) CHAPTER 4, LESSON 2 : POLYGONS AND CONGRUENCE Polygon A connected set of at least three line segments in the same plane such that each line segment intersects exactly two others, one at each endpoint. ● Sides - Line segments ● Vertices - Endpoints Congruent Two triangles are congruent iff there is a correspondence between their vertices such that all of their corresponding sides and angles are equal. Corollary to Congruent Triangles Two triangles congruent to a third triangle are all congruent to each other. CHAPTER 4, LESSON 3 : ASA AND SAS CONGRUENCE SAS and ASA Side-Angle-Side and Angle-Side-Angle ASA Postulate If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent. SAS Postulate If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent. CHAPTER 4, LESSON 4 : CONGRUENCE PROOFS Corresponding Parts “Corresponding parts of congruent triangles are equal.” CHAPTER 4, LESSON 5 : ISOSCELES AND EQUILATERAL TRIANGLE Defined By Its Sides, A Triangle Is... ● ● ● Defined By Its Angles, A Triangle Is... ● ● ● ● iff it has no equal sides iff it has at least two equal sides iff all of its sides are equal iff it has an obtuse angle iff it has a right angle iff all if its angles are acute iff all of its angles are equal Theorem 9 If two sides of a triangle are equal, the angles opposite them are equal. The converse of this statement is also true. Theorem 10 If two angles of a triangle are equal, the sides opposite them are equal. Corollaries to Theorems 9 & 10 An equilateral triangle is equiangular. The converse is true. CHAPTER 4, LESSON 6 : SSS CONGRUENCE Theorem 11 If the three sides of one triangle are equal to the three sides of another triangle, the triangles are congruent. SEMESTER2 CHAPTER 5, LESSON 1 : PROPERTIES OF INEQUALITY The “Three Possibilities” Property Either , , or The Transitive Property If and The Addition Property If then + > + The Subtraction Property If > , then - > - The Multiplication Property If > , and > 0, then The Division Property If > , and > 0, then The Addition Theorem of Inequality If > and > , then + > + The “Whole Greater than Part” Theorem If > , > , and + = , then > and > The whole is greater than the part. , then > > (these are fractions) CHAPTER 5, LESSON 2 : THE EXTERIOR ANGLE THEOREM ∠1 and ∠2 Rule ∠2 is larger. ∠1 is your interior angle. ∠2 is exterior. Exterior Angle of a Triangle An exterior angle of a triangle is an angle that forms a linear pair with an angle of the triangle. (Not vertical angle! Vertical angles are always equal. Exterior and interior angles do not equal the same.) Theorem 12 An exterior angle of a triangle is greater than either remote interior angle. CHAPTER 5, LESSON 3 : TRIANGLE SIDE AND ANGLE INEQUALITIES Theorem 13 If two sides of a triangle are unequal, the angles opposite them are unequal in the same order. Theorem 14 If two angles of a triangle are unequal, the sides opposite of them are unequal in the same order The Relationship between Theorems 13 and 14 They are the converses of each other. (They are the reversed versions of each other) CHAPTER 5, LESSON 4 : THE TRIANGE INEQUALITY THEOREM Theorem 15 (Triange Inequality Theorem) The sum of any two sides of a triangle is greater than the third side.
