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# GeometryLesson1

### Grade 10 Keystone

Question | Answer |
---|---|

Acute Angle | Any angle measuring less than 90* |

Addition Property | A property of equalities (equations) that allows you to add the same number on both sides and still have a true statement. Used in solving equations. |

Angle Addition Postulate | A rule stating that if I is in the interior <ABC, then m<ABI + m<IBC = m<ABC. |

Angle Bisector | A ray on an angle's interior that cuts the angle in half. We say it cuts the angle into 2 congruent angles. |

Angle | The intersection of 2 rays, when the rays intersect only at their endpoints. |

Area | A number describing a number of square units that can fit inside a figure. Example: the area of a rectangle is l x w. |

Between | Point B is between 2 other points A and C if all 3 are collinear, and the distance from A to B plus the distance from B to equals the distance from A to C. In symbols AB + BC = AC. |

Collinear | Points lying on the same line. Any 2 points are collinear. |

Compass | A device used to draw circles, or parts of circles called arcs. |

Complementary Angles | Angles whose measures add to 90* |

Conclusion | The "then" part of an if-then statement statement or conditional. q is the conclusion of p -> q |

Conditional Statement | Sometimes called a conditional. An if-then statement, p -> q |

Congruent Angles | Angles with equal measure. If m<A = m<B, then <A =~ <B. |

Congruent | 2 segments are congruent if they have the same length. _AB =~ _CD if AB = CD. |

Conjecture | An educated guess about some principle in math. Should be proven before it is assumed to always be true. |

Construction | Drawing a geometric figure using only a compass and a straightedge. |

Contrapositive | A new conditional formed by reversing the order like a converse, and then negating both parts like an inverse. CP of p-> q is q-> p. Unlike other rearrangements of a conditional, CP always has the same truth or falsehood as the original conditional. |

Converse | The reverse of a conditional. The converse of p -> q is q -> p. |

Coordinate Plane | A grid determined by the horizontal x-axis and the vertical y-axis. Any location on a plane can be described using an (x,y) coordinate system. |

Coplanar | 2 or more figures that lie in the same plane. |

Counterexample | An example, argument, or picture that shows a conjecture isn't always true. Only one counterexample is needed to prove a conjecture false. |

Deductive Reasoning | A thinking process where we apply a general rule to a specific situation. |

Degree | A unit of measure of angles. A full circle contains 360* |

Distance Formula | If given 2 points on a plane, (x1, y1) and (x2, y2), the distance between them is d= √(x2-x1)2 + (y2-y1)2. |

Distributive Property | An algebraic property that allows you to mutiply a single number by the sum of 2 or more numbers. a(b + c) = ab+ac |

Division Property | A property of equalities (equations) that allows you to divide by the same number on both sides and still have a true statement. Used in solving equations. |

Draw a Diagram | A problem solving strategy. Difficult problems are often made easier by drawing a diagram or picture. |

Exterior of an Angle | A point is on the exterior of an angle if it lies outside the 2 rays forming the angle. |

Hypotenuse | The longest side of a right triangle. The side opposite the right angle. |

Hypothesis | The "if" part of the if-then statement or conditional. |

If-Then Statement | A conditional statement consisting of a hypothesis followed by a conclusion. These can be written p -> q. |

Inductive Reasoning | A thinking process where we apply specific observations to a more general situation. |

Informal Proof | A paragraph proof that is less formal proof written in a paragraph form. Each statement much still be backed up by an accepted truth. |

Interior of an Angle | A point is on the interior on an angle if it lies on a segment connecting non-vertex points on each ray forming the angle. Think of it as inside 2 rays. |

Inverse | The negating of each part of a conditional. The inverse of p ->q is p -> q. |

Laws of Detachment | A rule that states: If p -> q is a true conditional, and p is true, then q is true. |

Law of Syllogism | A rule that states: If p -> q and p -> r are true conditionals, then p -> r is also true. |

Leg | One of the shorter sides of a right triangle. |

Line | A boundless set of points in one direction, as with a number line. Think of it as an infinitely long and thin length of wire. |

List the Possibilities | A systematic list of all ways a group of objects, letters, or numbers can be arranged. ABC can be listed: ABC, ACB, BAC, BCA, CAB, and CBA. |

Look for a Pattern | A problem solving strategy. Making a table or listing numerical results until a pattern is found often makes difficult problems easier. |

Measure of an Angle | The measure of an angle is the number of degrees separating the 2 rays the define it. We write m<A to stand for the number of degrees. |

Measure | The length of a segment _AB, which is written AB. |

Midpoint Formulas | On a number line, if m is the midpoint of a and b, the coordinate of m is (a + b)/2. On the plane, if M is the mis point of A(x1, y1) and B(x2, y2) the coordinates of M are [x1 + x2/2 , y1 + y2/2]. |

Midpoint Theorem | is M is the midpoint of _AB, then _AM =~ _MB. |

Midpoint | The middle of a segment. If M is the midpoint of _AB, M must be between A and B and AM = MB. |

Multiplication Property | A property of equalities (equations) that allows you to multiply the same number on both sides and still have a true statement. Used in solving equations. |

Negation | The denial of a statement. The negation of "A is red" is "A is not red." The negation of p is ~p. |

Non-collinear | 3 or more points not lying on the same line. |

Obtuse angle | Any angle measuring less than 180*, but more than 90*.` |

Opposite Rays | 2 rays that together form a straight line |

Ordered Pair | A specific location on a coordinate plane determined by the first (horizontal) x-coordinate and the second (vertical) y-coordinate. |

Origin | The center of a coordinate plane. The intersection of the x and y axis (0,0) |

Paragraph Proof | An informal proof that is a less formal proof written in paragraph form. Each statement still must be backed up by an accepted truth. |

Perimeter | A number describing the number of units of length that are needed to fit around the outside of a figure on the plane. For example, the perimeter of a rectangle in 2l + 2w. |

Perpendicular Lines | Lines that intersect at right angles. |

Plane | A boundless set of points in 2 directions, usually the x and y directions. Think of it as an infinitely large piece of perfectly flat paper. |

Point | A single location on a line, plane, or space. Think of it as an infinitely small dot made by your pencil. |

Postulate | A commonly accepted rule in mathematics that is so basic it can't be proven other postulates or theorems. |

Proof | A logical argument in which each step is backed up by an accepted truth. |

Protractor Postulate | A rule stating that given a ray and a degree measure, there is a unique second ray that will form an angle with the first ray with that measure. |

Protractor | A semicircular device used to measure angles. |

Pythagorean Theorem | A rule relating the sides of a right triangle. If the legs are a and b, and the hypotenuse is c, the a2 + b2 = c2. |

Quadrants | The 4 regions determined by the x and y axes, named by Roman Numerals. Quadrant I is in the upper right, and II, III, and IV are counter-clockwise from there. |

Ray | A line cut in half. Ray AB, written _AB, is the set of all points that are on the same side of A as is B. |

Reflexive Property | An algebraic property that states that a = a. |

Right Angle | An angle measuring 90*. |

Ruler Postulate | A rule stating that any 2 points on a number line can be reassigned to 0 and 1 for out connivence. |

Segment Addition Postulate | A rule stating that if B is between A and C, then AB + BC = AC, and if AB + BC = AC, then B is between A and C. |

Segment Bisector | Any segment, line, or plane, that curs a segment into 2 equal lengths. It must therefore pass through the segments midpoint. |

Side of an Angle | One of the two non-collinear rays that make up the angle. |

Space | A boundless set of points in 3 directions or dimensions, "3D". The directions are usually the x and y from a plane, with a z-axis perpendicular to the plane. |

Straightedge | Any device used to draw straight lines, such as a ruler, but unlike a ruler, it cannot be used to measure length. |

Substitution Property | An algebraic property that allows you to replace one expression for another that is known to be equal. If x = y, then for 2x + y = 7, you must say 2y + y = 7. |

Subtraction Property | A property of equalities (equations) that allows you to subtract the same number on both sides and still have a true statement. Used in solving equations. |

Supplementary Angles | Angles whose measures add to 180*. |

Symmetric Property | An algebraic property that states if a = b, the b = a. |

Theorem | A rule in mathematics that can be proven from other postulates or theorems. |

Three-dimesional Figures | Any figure existing in 3 dimensions. The directions are usually the x and y from a plane, with a z-axis perpendicular to the plane. Examples are cubes, cones, and pyramids. (See also space) |

Transitive Property | An algebraic property that states if a = b and b = c, then a = c. |

Two-Column Proof | A formal proofs where statements are listed in the left columns, and their reasons are listed in the right column. |

Vertex of an angle | The single points where the 2 rays that make up an angle intersect. |

X-Axis | The horizontal number line on a coordinate plane. |

X-Coordinate | The number specifying the horizontal location of a point in a coordinate plane. |

Y-Axis | The vertical number line on a coordinate plane. |

Y-Coordinate | The number specifying the vertical location of a point in a coordinate plane. |

Created by:
jsmusic3