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# GeometryLesson1

### Grade 10 Keystone

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