Geometry
similarity transformation
A dilation or a composition of rigid motions and dilations
Reduction
A dilation with a scale factor less than 1.
Angle
A figure formed by two rays with a common endpoint.
Plane
A flat surface that extends without end and has no thickness.
If the sum of two angles is an obtuse angle, at least one of the angles must be
Acute
Theorem 6-21 trapezoid midsegment theorem
If a quadrilateral is a trapezoid, then the midsegment is parallel to the bases, and the length of the midsegment is half the sum of the length of the two bases.
Theorem 6-20
If a quadrilateral is an isosceles trapezoid, then it's diagonals are congruent.
Theorem 6-9
If an angle of a quadrilateral is supplementary to both of its consecutive angles then the quadrilateral is a parallelogram.
Theorem 7-1 Side - angle - side similarity (SAS ~)
If an angle of one triangle is congruent to an angle of a second triangle, and the sides that include the two angles are proportional, then the triangles are similar.
Theorem 7-1 Side-Angle-Side Similarity (SAS~)
If an angle of one triangle is congruent to an angle of a second triangle, and the sides that include two angles are proportional, then the triangles are similar.
Theorem 7-2 Side-Side-Side (SSS~)
If the corresponding sides of two triangles are proportional, then the triangles are similar.
Congruent complements theorem
If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent.
Tangent
Length of leg opposite the angle/length of the adjacent to the angle.
Theorem 11-10 surface area of sphere
The surface area of a sphere is four times the product of pi and the square of the radius of the sphere. (4 • pi • r^2)
adjacent angles
Two coplanar angles that share a common side, the same vertex and and no common interior points.
Dilation
a transformation that enlarges or reduces the original figure proportionally.
right triangle
a triangle with a right angle.
right angle
an angle that measures 90 degrees.
straight angle
an angle that measures exactly 180 degrees.
Coordinates
are numbers or letters that specify the location of an object.
Image
the figure you get after a transformation.
Leg
the sides that form the right angle in a right triangle
Verify (v)
to establish the truth or accuracy of,confirm
Midpoint Formula
(X1+x2/2,Y1+y2/2) To determine: The coordinates on the midpoint of a side And whether diagonals bisect each other
Verify
(v.) to establish the truth or accuracy of, confirm
Midpoint formula
(x₁+x₂)/2, (y₁+y₂)/2
Reflexive properties of a Equality
A =A
conditional statements
A If-then statement. (p--->q) The hypothesis is the part p following if. The conclusion is the part q following then. Read as "if p then q" or "p implies q".
Trapezoid
A Quadrilateral with exactly one pair of parallel sides.
Bisector
A bisector is something that cuts an object into two equal parts. It is applied to angles and line segments.
Circle
A circle is a simple closed shape in Euclidean geometry. It is the set of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant.
Circumscribed
A circumscribed circle or circumcircle passes through all vertices of a plane figure and contains the entire figure in its interior. The center of this circle is called the circumcenter.
Ratio
A comparison of two quantities by division.
Reflections across interesting lines
A composition of reflections across two intersecting lines is a rotation.
Reflection across parallel lines
A composition of reflections across two parallel lines is a translation.
True
A coordinate plane extends without end and has no thickness.
Two column proof
A formal proof that contains statements and reasons organized in two columns./has numbered statements and corresponding reasons that show an argument in a logical order
conjecture
A guess or a prediction/ a conclusion reached by using deductive reasoning.
line of reflection
A line that a figure is reflected or flipped across to create a mirror image of the original figure.
Medians
A median of a triangle is a segment whose endpoints are a vertex and the midpoint of the opposite side./ intersect at a Centroid.
Indirect measurement
A method of measurement that uses formulas, similar figures, and/or proportions
Transformation
A movement of a geometric figure.
vertical angles
A pair of opposite congruent angles formed by intersecting lines/two nonadjacent angles formed by two intersecting lines/ two angles whose sides are opposite rays.
Rectangle
A parallelogram with 4 right angles.
Square
A parallelogram with 4congruent sides and 4 right angles.
Rhombus
A parallelogram with four congruent sides
Square
A parallelogram with four congruent sides and four right angles.
Rectangle
A parallelogram with four right angles
altitude of a triangle
A perpendicular segment from a vertex to the line that is the opposite side.
Altitudes
A perpendicular segment from the vertex to the side opposite the vertex/intersect at Orthocenter
coordinate proof
A proof involving placing geometric figures in a coordinate plane/A style of proof that uses coordinate geometry and algebra.
Trapezoid
A quadrilateral with exactly one pair of parallel sides
Straightedge
A ruler with no numbers or markings on it.
Midsegment
A segment that connects the midpoints of two sides of a geometric figure.
Diagonal
A segment with endpoints in nonadjacent vertices of a polygon.
Locus
A set of points, all of which meet a stated condition./A locus of points is the set of points, and only those points, that satisfies given conditions. The locus of points at a given distance from a given point is a circle whose center is the given point and whose radius is the given distance.
Theorem
A statement or conjecture that can be proven.
Biconditional
A statement that reads p if and only if q./ a statement that combines (p➡️q) and (q➡️p) as (p↔️q)
extended proportion
A statement where three or more ratios are equal.
Diameter
A straight line passing from side to side through the center of a circle or sphere.
coordinate proof
A style of proof that uses coordinate geometry and algebra and is a type a proof that involves placing geometric figures in a coordinate plane.
similarity transformation
A transformation that produces similar figures./A dilation or a composition of rigid motions and dilations (two figures are similar if and only if there is a similarity transformation that maps one figure onto the other.)
Reflection
A transformation which flips a figure over a line of reflection resulting in a mirror image of the original figure. Therefore orientation of the figure reverses.
Rotation
A transformation which turns a figure about a fixed point called the center of rotation.
Plane
A two-dimensional flat surface that extends in all directions/ a flat, two-dimensional surface that extends infinitely far. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space.
vertical line
A vertical line is one the goes straight up and down, parallel to the y-axis of the coordinate plane. ... In the figure above, drag either point and note that the line is vertical when they both have the same x-coordinate. A vertical line has no slope. Or put another way, for a vertical line the slope is undefined.
Theorem 2-4
All right angles are congruent.
Exterior angle
An angle formed by one side of a polygon and the extension of an adjacent side
obtuse angle
An angle that measures more than 90 degrees but less than 180 degrees
Theorem 12- 16 equation of a circle
An equation of a circle center (h,k) and a radius r is (x-h)^2 +(y-k)^2 = r^2.
Proportion
An equation stating that two ratios are equal.
Theorem 8-6 30-60-90 Triangle
And a 30 -60-90 triangle, The length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is 3 squared rooted times length of the shorter leg.
corresponding angles
Angles that lie on the same side of a transversal t and in corresponding positions.
Indirect measurement
Any method that uses formulas, similar figures, and/or proportions to measure an object/A way to use the properties of similar figures to find measurements.
Locus of the x and y axises
Are angle bisectors at the vertex of each axis/ will form another set of intersecting lines.
Consecutive
Are items that follow one another and on interrupted chronological logical order. Math usage: consecutive angles of a polygon share a common side.
Parallel
Are lines extending in the same direction and at the same distance apart/Lines that line the same plane but never intersect, no matter how far they extend out into space./ coplanar lines that do not intersect.
Variable coordinates
Are single-dimension arrays that have the same size as the dimension they are assigned to. A coordinate array represents the data coordinates for each index in the named dimension. These arrays contain monotonically increasing or decreasing values. The & character is used to reference and assign coordinate variables.
Leg
Are the sides are form the right angle in a right triangle.
Circumference
C=2πr/ the distance going around the circle.
Related conditional statements 1
Conditional: use given hypothesis and conclusion. (p--->q). It reads as if p then q.
Theorem
Conjecture or statement that you prove true/you use definitions, postulates, properties, and previously proven theorems to prove Theorems
Related conditional statements
Contrapositive: Negate both the hypothesis and the conclusion of the converse of the conditional (~q--->~p). It reads as if not q, then not p.
Related conditional statements 2
Converse:Exchange the hypothesis and the conclusion of the conditional.(q--->p). It reads as if q, then p.
Locus of two points
Creates a form of perpendicular bisector that is between both points./the perpendicular bisector of the line segment determined by the two points.
Bisector
Divides a whole into two equal parts.
Bisector
Divides a whole into two equal parts/it's a point, segment, ray, or line that divides an angle or a segment into two congruent angles or segments
Ruler Postulate
Every point on a line an be paired with a real, called the coordinate of the point.
Law of Cosines
For any triangle with the side lengths A, B, and C opposite angles a, b,and c,respectively, the law of cosines relates to the measures of the triangles according to the following equations. a²=b²+c²-2bcCos A/ b^2= a^2 +c^2- 2acCos B/ c^2= a^2 +b^2 -2abCos C/ used to solve a triangle if sas or sss are present.
geometric mean
For any two positive numbers ("a" and "b"), did geometric mean of those numbers is a positive number ("x") such that a/x = x/b (Number that when substituted for X will make a porportion true)/ the central number in a geometric progression (e.g., 9 in 3, 9, 27 ), also calculable as the n th root of a product of n numbers.
geometric mean
For any two positive numbers a and b, the geometric mean of a and b is the positive number x such that a/x = x/b.
180 degree rotation
From (x,y) goes to (-x,-y)
90 degree rotation
From (x,y) goes to (-y,x)
360 degree rotation
From (x,y) goes to (x,y)
270 degree rotation
From (x,y) goes to (y, -x)
Midpoint formula on a coordinate plane
Given A( x1, y1) and B(x2, x y2), the coordinates of the midpoint of segment AB are M(x₁+x₂)/2, (y₁+y₂)/2.
Addition property of equality
If A = B, then A + C = B + C.
Theorem 6-19
If I Quadrado is an isosceles trapezoid, then each pair of a base angles are congruent.
Theorem 6-22
If I quadrilateral is a kite, then it's diagonals are perpendicular.
Theorem 6-4
If I quadrilateral is a parallelogram, then it's consecutive angles are supplementary.
Segment Addition Postulate
If Three points A,B, and C are collinear is between A and C, then AB + BC = AC.
Subtraction properties of equality
If a = B, then a- c = b- c
Division property of equality
If a = b and c ≠ 0, then a/c = b/c
Symmetric property of equality
If a = b, then b = a
Substitution property of equality
If a equals B, then B can replace a in any equation.
Theorem 7-4 Side-Splitter Theorem
If a line is parallel to one side of a triangle and intersects the other two sides, then it divides the sides proportionally.
Side-Splitter Theorem
If a line is parallel to one side of triangle and intersects the other two sides, then it divides the two sides proportionally.
Theorem 6-3
If a quadrilateral is a parallelogram, then it's opposite sides are congruent.
Theorem 6-6
If a quadrilateral is a parallelogram, then its diagonals bisect each other.
Theorem 6-5
If a quadrilateral is a parallelogram, then its opposite angles.
Trapezoid Midsegment Theorem
If a quadrilateral is a trapezoid, then the midsegment is parallel to the bases and the the length of the midsegment is half the sum of the length of the bases.
Triangle-Angle-Bisector Theorem
If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.
Pythagorean Theorem
If a triangle is a right triangle, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. (a²+b²=c²)
Multiplication property of equality
If a=b, then a*c=b*c
Theorem 06-10
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Theorem 6-8
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Point
If distinct lines intersect,then they intersection exactly
Line
If distinct planes intersect,then they intersect at exactly one
Theorem 6-17
If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus.
06-12
If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.
Theorem 7-2 Side - side - side similarity (SSS~)
If the corresponding sides of two triangles are proportional, then the triangles are similar.
Theorem 6-18
If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
Theorem 6-16
If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
Theorem 6-18
If the diagonals of parallelogram are congruent, then the parallelogram is a rectangle.
Law of Detachment
If the hypothesis of a true conditional is true, then the conclusion is true. Conversely, If a conditional is true and its hypothesis is true, then its conclusion is true./ a form of deductive reasoning. If p➡️q is true and p is true, then q is true.
Theorem 6-17
If the one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus.
Theorem 11-12 Areas and Volumes of similar Solids
If the scale factor of two similar solids is a:b, then • the ratio of their corresponding areas is a^2:b^2 • the ratio of their volumes is a^3:b^3
Theorem 8-3
If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, then triangle is obtuse.
Theorem 8-3 Pythagorean inequality theorem
If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the two other sides, then the triangle is obtuse.
Theorem 8-4
If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is acute.
Theorem 8-4 Pythagorean inequality Theorem
If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is acute.
Converse of the Pythagorean Theorem
If the sum of the squares of the lengths of the two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle.
Converse of the Pythagorean theorem
If the sum of the squares of the lengths of the two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle.
corollary to the Side-SplitterTheorem
If three parallel lines intersect two transversals then the segments intercepted on the transversals are proportional
Corollary to the side-splitter theorem
If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.
Congruent Supplements Theorem
If two angles are supplements of the same angle or (of congruent angles), then the two angles are congruent.
Linear Pair Postulate
If two angles form a linear pair, then they are supplementary.
Postulate 7-1 A angle angle similarity (AA~)
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Postulate 7-1 Angle-Angle Similarity (AA~)
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
5-10 theorem
If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.
Theorem 5-13 Hinge Theorem (SAS inequality)
If two sides of one triangle are congruent to two sides of another triangle and the included angles are not congruent, The longer third side is opposite the larger included angle.
Theorem 5-14 Converse of the Hinge Theorem (SSS inequality)
If two sides of one triangle are congruent to two sides of another triangle and the third sides are not congruent, the larger included angle is opposite the larger third side.
Theorem 8-5 45-45-90 Triangle Theorem
In a 45-45-90 triangle, both legs are congruent and the length of the hypotenuse is 2 square rooted times the length of a leg.
Theorem 12-9
In a circle, if a diameter bisects a chord (that is not the diameter), then it is perpendicular to the chord.
Theorem 12-8
In a circle, if a diameter is perpendicular to a chord, then it bisects the cord and it's arc.
Theorem 12- 10
In a circle, the perpendicular bisector of a chord contains the center of the circle.
Cross multiply property 1
In a proportion a/b=c/d, where b does not equal 0 and d does not equal 0, the product of the extremes a and d equals the product of the means b and c.
Cosine
In a right triangle, it is the ratio of the side adjacent to a given acute angle to the hypotenuse.
Sine
In a right triangle, it is the ratio of the side opposite a given an acute angle to the hypotenuse.
Locus of a line
In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.
Locus of a line segment
In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.
means of a proportion
In the proportion a/b = c/d, b and c are the means/ the middle terms in the proportion.
Extremes of Proportion
In the proportion a/b=c/d, a and d are the extremes/the first and last terms of a proportion.
Same-side interior angles
Interior angles that lie on the same side of the transversal.
related conditional statements 3
Inverse: Negate both the hypothesis and the conclusion of the conditional (~p--->~q). It reads as if not p, then not q.
Hinge
Is a device on which something else depends or turns./ means to depend on.
Rigid motion
Is a geometric transformation in which the size and shaped the geometric figure does not change.
bi
Is a prefix means having two.
Parallelogram
Is a quadrilateral with two pairs of opposite sides parallel. Opposite sides may have include arrows to show the sides are parallel
Hemisphere
Is an exact half of a sphere.
Sphere
Is formed by the revolution of a circle about its diameter/is the set of all points in space equal distance from a given point called the center.
The converse of a theorem
Is not always true
Cosine
Length of leg adjacent to the angle/ length of the hypotenuse.
Sine
Length of leg opposite the angle/ length of the hypotenuse.
Skew
Lines that are noncoplanar;are not parallel and do not intersect.
complement
Math Usage: when the measures of two angles have a sum of 90, each angle is a complement of the other.
Perpendicular
Means are right angles to a given line or plane./
Consecutive
Means following in order without interruption
indirect
Means means not direct in the course or action, taking a roundabout route to get to a point or idea.
Concurrent
Means occurring or existing the same time. When 3 or more lines intersect in one point, they are concurrent.
Deduce
Means to use known facts to reach a conclusion.
Inscribed
Means written, marked, or engraved on. Circumscribed means encircled, confined, limited, Math Usage: An inscribed angle is formed by two chords with a vertex on the circle.
Midpoint
Of a segments a point that divides a segment into two congruent segments.
scale drawing
Represents an object as smaller than or larger than its actual size
Chord
Segment whose endpoints are on a circle.
Space
Set of all points and three dimensions
Law of Sines
SinA/a = SinB/b = SinC/c (for any triangle with the lengths of the sides opposite angles A, B, and C be a, b, and c, respectively. Then the law of sines relates to sine of each angle to the length of its opposite side./ used to solve Triangle with SSA or ASA side angle patterns.
Trigonometric ratios
Sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot).
Indirect proof
Step one: State as a temporary assumption opposite (negation) of what you want to prove. Step two: Show that this temporary assumption leads to contradiction. Step Three: conclude that the temporary assumption must be be false and what you want to prove must be true.
5-12 theorem Triangle inequality theorem
Sum of the length of any two sides of a triangle is greater than the length of the third side.
Angle of depression
The angle between the line of sight and the horizontal when an observer looks downward./The angle formed by a horizontal line and a line of sight to a point below.
Angle of elevation
The angle between the line of sight and the horizontal when an observer looks upward/the angle formed by a horizontal line and a line of sight to a point above.
Locus of an angle
The angle bisector of the angle.
Theorem 5-7
The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides of the triangle.
Midpoint formula on a number line
The coordinate of the midpoint M of segment AB with endpoints at a and b a+b/2
Locus of a Circle
The definition of a circle locus of points a given distance from a given point in a 2-dimensional plane. The given distance is the radius and the given point is the center of the circle.
The Distance Formula
The distance between two points A(x1, y1) and B(x2, y2) is
Conclusion
The end of event or the last step of a reasoning process.
Space
The infinite extension of the three-dimensional region in which all matter exists.
Interior
The inside of geometric figure./ the region between two parallel lines.
Great circle
The intersection/cross section of a sphere and a plane that contains the center of the sphere. /A circle that divides the globe in half or marks its circumference.
Distance
The length of a path or the space between between two points on a line.
Theorem 5-9 Concurrency of Altitudes Theorem
The lines that contain the altitudes of a triangle are congruent. The point of concurrency is the Orthocenter of the triangle. The Orthocenter center of a triangle can be inside, on, the outside triangle. Acute: inside the triangle. Right: at the vertex. Obtuse: outside the triangle.
Locus of two parallel lines
The locus equidistant from two parallel lines, m1 and m2, is a line parallel to both m1 and m2 and halfway between them. This theorem asks you to "describe the path formed by all points the same distance from two parallel lines". ANSWER: The path will be 1 line halfway between the parallel lines.
hypotenuse of a right triangle
The longest side of a right triangle / The side across from the right angle
Corollary to the Triangle Sum exterior Angle Theorem
The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles.
Probability
The measure of the likelihood that event will occur.
5-8 Concurrency of Medians Theorem
The medians of triangle concurrent at a point (The centroid of the triangle) that is two thirds the distance from each vertex to the measure midpoint of the opposite side.
Converse
The opposite of something.
preimage
The original figure before a transformation.
Theorem 5-6 Concurrency of perpendicular Bisectors Theorem
The perpendicular bisectorsof the sides of a triangle are concurrent at a point equidistant from the vertices.
deductive reasoning
The process of using logic to draw conclusions/reasoning from the general to the specific.
scale factor
The ratio of any two corresponding lengths in two similar geometric figures/A scale written as a ratio without units in simplest form.
scale factor
The ratio of any two corresponding lengths of their corresponding sides in two similar geometric figures./ for two similar solids is the ratio of their corresponding linear dimensions.
Standard form
The standard form of an equation gives information that can help you graph the Quetion in the coordinate plane. Example: The standard form of an equation of a circle is (x-h)^2 +(y-k)^2 = r^2. The standard form of a linear equation is Ax + By = C. The standard form of a quadratic equation is y= ax^2 + bx +c.
coordinate geometry
The study of geometry on a coordinate grid/is the study of algebraic equations on graphs. An example of coordinate geometry is plotting points, lines and curves on an x and y axis.
Theorem 6-1 (Polygon Angle-Sum) and corollary
The sum of the measures of interior of an n-gon is (n - 2)180. The measure of each interior angle of regular n-gon is (n - 2)180/n
Theorem 11-11 volume of a sphere
The volume of a sphere is 4/3 of the product of pi and the cube of the radius of the sphere.(4/3 • pi • r^3)
Proof
The writing of reasoned, logical explanations that use definitions, axioms, postulates, and previously proved theorems to arrive at a conclusion about a geometric statement.
Variable coordinates
These ancillary data are divided up into three categories: variable attributes, dimensions, and coordinates. Variables can have an unlimited number of attributes assigned to them. Each dimension of a variable can have a name associated with it and optionally a coordinate variable.
Plane
Through any three noncollinear points there is exactly one
Line
Through any two points there is exactly one
Compare
To compare is to examine two or more items, noting similarities and differences.
similar triangles
Triangles that have the same shape but that may or may not be the same size.
complementary angles
Two angles whose measure have a sum of 90 degrees.
supplementary angles
Two angles whose measures a sum of 180 degrees.
Congruent
Two figures are congruent if and only if there is a sequence of rigid motions that maps one figure onto the other.
True
When you name ame angles angles using using th three points, the vertex gets named first.
Theorem 12-7
Within a circle or in congruent circles, chords equidistant from the center or centers of a circle are congruent.
Converse of Theorem 12-4
Within a circle or in congruent circles, congruent arcs have congruent central angles.
Converse of Theorem 12-6
Within a circle or in congruent circles, congruent arcs have congruent chords.
theorem 12-4
Within a circle or in congruent circles, congruent central angles have congruent arcs.
Theorem 12-5
Within a circle or in congruent circles, congruent central angles have congruent chords.
Converse of Theorem 12-7
Within a circle or in congruent circles, congruent chords equidistant from the center (or centers) of a circle.
Theorem 12-6
Within a circle or in congruent circles, congruent chords have congruent arcs.
Converse of Theorem 12-5
Within a circle or in congruent circles, congruent chords have congruent central angles.
Law of Syllogism
You can state a conclusion from two true conditional statements when the conclusion of one statement is hypothesis of another statement. If p->q and q->r are true statements, then p->r is a true statement.
Reason
a cause, explanation, or justification for an action or event./ clear, ordered or a logical kind of thinking.
enlargement
a dilation with a scale factor greater than 1.
scale drawing
a drawing that is the same shape as the object it represents but also represents an object as smaller than or larger than its actual size.
Perpendicular bisector
a line segment perpendicular to and passing through the midpoint of (left figure). The perpendicular bisector of a line segment can be constructed using a compass by drawing circles centered at and with radius and connecting their two intersections.
Transversal
a line that intersects two or more other, coplanar lines at different points.
Rhombus
a parallelogram with 4 congruent sides
regular polygon
a polygon that is both equilateral and equiangular
Kite
a quadrilateral with exactly two distinct pairs of congruent consecutive sides/ diagonals are perpendicular.
angle bisector
a ray that divides an angle into two congruent angle/ intersect at Incenter
angle bisector
a ray that divides an angle into two congruent angles.
Pythagorean triple
a set of three positive integers that work in the Pythagorean theorem./Set of 3 nonzero whole numbers a, b, and c that satisfy the Pythagorean Theorem.
Compass
a technical drawing instrument that can be used for inscribing circles or arcs. As dividers, they can also be used as tools to measure distances, in particular on maps.
Cross products property 3
a/b=c/d is equivalent to a+b/b=c+d/d.
cross products property 2
a/b=c/d is equivalent to a/c=b/d.
acute angle
an angle that measures less than 90 degrees and more than 0 degrees.
Distance formula
d = √[( x₂ - x₁)² + (y₂ - y₁)²]
Distance Formula
e To congruent diagonals sides determine are whether are congruentthe
Proof
evidence
similar figures
figures that have the same shape but not necessarily the same size.
Transitive property of equality
if a = b and b = c, then a = c
Comparison Property of Inequality
if a=b+c and c>0, then a>b
06-11
if the diagonals of a quadrilateral bisect each other then, the quadrilateral is a parallelogram.
Theorem 2-5
if two angles are congruent and supplementary, then each is a right angle.
cross products property
in a proportion, the product of the extremes equals the product of the means.
perpendicular bisector
is a special kind of segment, ray, or line that. (1) intersects a given segment at a 90° angle, and. (2) passes through the given segment's midpoint./intersects at circumcenter.
Translation
is a term used in geometry to describe a function that moves an object a certain distance. The object is not altered in any other way. It is not rotated, reflected or re-sized. ... In a translation, every point of the object must be moved in the same direction and for the same distance.
paragraph proof
is a two-column proof written in sentences.
Hypothesis
is the "if" part (antecedent) of a conditional statement.
Elevation
is the height above a given level, such as I level or sea level. Math usage: angles of elevation and depression are cute angles of right triangles formed by a horizontal distance and a vertical height.
radius of a circle
is the line segment connecting the center of the circle to any point on the circle.
Proportion
is the relationship between two things when the quantities of the two are equal in ratios. An example of geometrical proportion is when 4 is to 2 as 8 is to 4 - a square 4x2 and a square 8x4.
Construction
means to draw shapes, angles or lines accurately. These constructions use only compass, straightedge (i.e. ruler) and a pencil.
inscribe
means to draw something inside something else. In geometry it usually means drawing one shape inside another so that it just touches.
Diagonals equation
n(n-3)/2 N=sides
Alternate exterior angles
nonadjacent exterior angles that lie on opposite sides of the transversal.
alternate interior angles
nonadjacent interior angles that lie on opposite sides of the transversal.
interior of an angle
noun, Geometry. 1. an angle formed between parallel lines by a third line that intersects them. 2. an angle formed within a polygon by two adjacent sides.
True
polygon has the same number of sides and vertices.
similar polygons
polygons that have the same shape but not necessarily the same size.
Inverse sine
the angle that has a sine equal to a given number. Synonyms: arc sine, arcsin, arcsine Type of: circular function, trigonometric function. function of an angle expressed as a ratio of the length of the sides of right-angled triangle containing the angle.
angle of rotation
the degree measure of the angle through which a figure is rotated.
center of dilation
the fixed point about which the figure is enlarged by or reduced by in a dilation.
Hypotenuse
the longest side of a right triangle/The side opposite the right angle in a right triangle.
Base
the lowest or bottom part of a geometric figure.
Trigonometry
the mathematics of triangles and trigonometric functions.
scale factor of a dilation
the ratio of the length of the preimage to the corresponding length in the image grows by or shrinks in during a dilation, with the image length always in the numerator. If the scale factor of dilation is greater than one, the dilation is an enlargement. If the scale factor is less than one, the dilation is a reduction.
coordinate geometry
the study of algebraic equations on graphs. An example of coordinate geometry is plotting points, lines and curves on an x and y axis.
Slope formula
y2-y1/x2-x1
True
you can use properties, postulates, and previously proven grams to verify steps in a proof