FULL GEOMETRY
SSS postulate:
A postulate stating that if the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.
ASA postulate
A postulate stating that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
AA similarity postulate
A postulate stating that if two angles of one triangle are congruent to two angles of a second triangle, then the triangles are similar.
SAS postulate:
A postulate stating that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
parallelogram
A quadrilateral in which both pairs of opposite sides are parallel.
Trapezoid
A quadrilateral with exactly one pair of parallel sides which is the base. it is NOT a parallelogram.
rhombus
A quadrilateral with four congruent sides.
square
A quadrilateral with four right angles and four congruent sides. Squares have all of the properties of parallelograms, rectangles, and rhombi.
rectangle
A quadrilateral with four right angles. Rectangles are parallelograms; opposite sides are parallel and congruent.
What is special about a radius that is perpendicular to a chord?
A radius that is perpendicular to the chord divides the chord into two equal pieces
major arc
An arc of a circle that is longer than half the circumference. The degree measure of a ____________ arc is greater than 180°.
minor arc
An arc of a circle that is shorter than half the circumference. The degree measure of a _______arc is less than 180°.
Postulates
Definition: A postulate or axiom is a statement that is assumed to be true without proof Example: Water is wet Example 2: A line segement can be drawn between any two points.
Proof
Definition: An argument you make to prove something is true. Example: AB=CD
Evidence is
Definitions postulates Common notions
Consecutive interior angles postulate
If two parallel lines are cut by a transversal, the _____________ angles are supplementary.
What is the flat plane postulate?
If you are given two points in a plane, then the line that goes through both points is also in that same plane. In other words, a plane is flat.
Transitive property.
In a chain of congruence statements, the first triangle is congruent to the last triangle.
"A" Right Triangle Similarity Theorem
In a right triangle, if the altitude is drawn from the vertex of the right angle to the triangle's hypotenuse, then the two right triangles formed are similar to the given triangle and to each other
Incenter
The incenter of a polygon is the center of the inscribed circle.
altitude of a triangle
The line segment from a vertex of a triangle that is perpendicular to the opposite side or to the line containing the opposite side.
median
The line segment that joins the midpoints of the legs of a trapezoid. The median is parallel to the bases, and its length equals the mean of their lengths..
hypotenuse:
The side across from the right angle in a right triangle. It is the triangle's longest side.
other then the circumference of a circle formula how might you describe the relationship between the radius and the circumference of a circle?
The size of the radius and the circumference are related. when the radius gets bigger, the circumference gets bigger by a factor of 2pi
area
The space taken up by a two-dimensional figure or surface. _______ is measured in square units, such as square inches, square centimeters, or square feet.
How could you show that two arcs are congruent?
Two arcs are congruent if they have the same length and belong to the same circle or two congruent circles.
When are two arcs congruent?
Two arcs of a circle are congruent if and only if their associated chords are congruent.
Two column proof
Two columns deductions on left reasons on right
How do you get an estimate of the circumference of a circle from the radius?
When given the radius of a circle, multiply that number by 6 to get a rough idea of its circumference.
Does law of sines work for all types of triangles?
Yes
Does the theorem SAS work?
Yes
Does the theorem SSS work?
Yes
If a chord is bisected by a radius, is the radius perpendicular to the chord?
Yes
When you make the diagonals congruent does the parallelogram become a rectangle?
Yes it does become a rectangle
can you use properties of a parallelogram on a rectangle?
Yes you can use them.
Rigid Transformation
a transformation that does not change the shapes angles and lengths
Common notion
Defenition: Something that is assumed most people know. Example: during day there is light.
Arc Length
the length of an arc of a circle
When are two chords congruent?
two chords are congruent if and only if their associated central angles are congruent.
_____________ Triangles can be inscribed in a given circle.
several
arc
A part of the circumference of a circle.
convex
Having no indentations.
The measures of opposite angles of a quadrilateral sum to
180
Corollaries
A corollary is a statement that naturally follows, or makes sense, based on something you have already proven. Has been proven directly ties to a previously proven statement generally accepted in the world of math.
circle
A geometric figure consisting of all the points on a plane that are the same distance from a single point, called its center.
there are three things you need to do to calculate the area of a sector
1. Find the area of the whole circle that contains the sector. 2. Find the fraction of the circle covered by the sector. 3. Multiply the area by the fraction.
Sector
A part of the interior of a circle bounded by an arc and two radii that share the arcs endpoints.
vertex
A point at which rays or line segments meet to form an angle.
what can you say about a polygon that does not have a circumscribed or a inscribed circle?
A polygon with no circumscribed or inscribed circle has no in center or circumcenter.
Indirect proof
A indirect proof is a proof when you assume the opposite is true. paragraph style opposite is assumed true contradiction is found.
secant
A line or a line segment that intersects a circle in two points.
diagonal
A line segment that connects two nonconsecutive vertices of a polygon..
diameter
A line segment that contains the center of the circle and has endpoints on the circle. This term also refers to the length of this line segment; the ______________of a circle is twice the radius.
radius
A line segment that has one endpoint at the center of a circle and the other endpoint on the circle. ___________ also means "the length of such a line segment." The _____________of a circle is half its diameter. The plural of _______________ is radii.
tangent line
A line that intersects a circle at exactly one point, known as the point of tangency.
Area
the space taken up by a two dimensional figure or surface. area is measured in square units.
If each vertex of a triangle touches a figure, then ________
the triangle is inscribed in the polygon
Inscribe
to fit one object tightly inside another.
Angle Bisector
An _________________ is a line or line segment that divides an angle in half.
tangent-chord angle
An angle formed by a tangent and a chord that shares the point of tangency. The measure of a tangent-chord angle is half the measure of the intercepted arc inside the angle.
inscribed angle
An angle formed by two chords of a circle that share an endpoint. It is not a central angle
Inscribed angle
An angle formed by two chords that share an endpoint on a circle.
central angle
An angle that has its vertex at the center of a circle.
chord
Any line segment whose endpoints are on the circle.
What is special about chords that are the same distance from the center?
Chords that are the same distance from the center of the circle have the same length.
regular polygons
Convex polygons in which all sides and angles are congruent.
Statements are
Given 1st Deduction or conclusion
concave
Having one or more indentations.
Acute circumcenter
Inside
How are the angles formed by the chords and the intercepted arcs related?
Intersecting chords form a pair of congruent vertical angles. Each angle measure is half the sum of the intercepted arcs.
Circumcenter
It has perpendicular bisectors that go through each side.
intercepted arcs
Parts of the circle (an arc) that are cut off from the rest of the circle's circumference by lines or segments intersecting the circle.
circumference
The distance around a circle
How do you find the distance between the center point and a chord?
The distance is the measure of the perpendicular bisector between the center point and the chord.
What is the relationship between the circle's height and circumference?
The length of the circumference is roughly three times the circle's height.
What is the measure of angles formed by intersecting chords?
The measure of an angle formed by intersecting chords is half the sum of the measures of the intercepted arcs.
describe how the measures of a central angle and a inscribed angle are related.
The measure of the central angle is twice as much as the inscribed angle will be. it also works in reverse.
Describe how the central angle measure relates to arc length and radius.
The measure of the central angle, in radians, describes the ratio between the arc length and the radius.
center of the circle
The point at the exact __________________. All points on a circle are the same distance from the _____________.
point of tangency
The point at which a tangent line meets a curve. In a circle, the radius ending at the point of tangency is always perpendicular to the tangent line..
what do you notice about the sector that can help you find the area of a circle?
The sector covers half of the circle.
the sector
The sector of a circle is bounded by a central angle of the circle and the intercepting arc.
what is the relationship between the circle and the vertices of an inscribed triangle?
The vertices of the triangle always touch the circle. many triangles can be inscribed in any one circle.
formula for finding the area of a parallelogram.
To find the area of a parallelogram, multiply the height and the length of its base.
True or false? If two chords are congruent, they are the same distance from the center of the circle.
True
Do congruent chords of a circle always create congruent arcs?
Yes, congruent chords of a circle always create congruent arcs.
Theorem
a statement that has already been proven to be true. has been proven generally accepted in the world of math
The opposite angles of a quadrilateral in a circumscribed circle are
always supplementary.
circumference of a circle formula
c=2pir
Flowchart proof
copy each statement from the two-column proof into a box in the flowchart. Then write the justification for each statement below the box. The first statement is usually the starting state given in the problem description
What can you say about the arcs of two congruent central angles
if two central angles of a circle are congruent then they form congruent arcs.
Incenter
it has angle bisectors, the lengths of the angle bisectors are the same.
_________ Circle(s) can be inscribed in a given triangle.
one
points that are equidistant from two sides of a triangle are__________?
points equidistant from two sides of a triangle are on the angle bisector of those two sides?
QED
quod Erat demonstrandum
how are the areas of a sector of a circle and the circle related?
the area of a sector is a fraction of the area of the circle.
Incenter
the center of the circle that can be inscribed in a given triangle.
if a circle is tangent to each side of an octagon, then___________
the circle is inscribed in the polygon.
Exterior angle theorem
the exterior angle is the sum of the remote interior angles.
explair how R compares to the height of the parallelogram.
the height of the parallelogram is almost equal to R.
Incenter is _______________________
the incenter of a tringle is the point that is equidistant from all sides.
what is the relationship between the measure of an inscribed angle and the measure of the arc that it intercepts.
the measure of an inscribed angle is half the measure of the arc it intercepts. it works in reverse.
What is the relationship between the radius and the tangent.
the radius is always perpendicular to the point of tangency.
Line segment
A part of a line with endpoints at both ends. The symbol AB means "the_________________ with endpoints A and B."
intercepted arc
A part of the circle (an arc) that is cut off from the rest of the circle's circumference by lines or segments intersecting the circle.
Vertex
A point at which rays or line segments meet to form an angle.
triangle
A polygon with three sides.
Obtuse angle
An angle with a measure greater than 90° but less than 180°.
Symbol for similar
~
vertical angles:
A pair of opposite angles formed by intersecting lines. Vertical angles have equal measures
vertical angles
A pair of opposite angles formed by intersecting lines. Vertical angles have equal measures.
Median length formula
1/2 (ab +cd)
perpendicular bisector
A line, ray, or line segment that bisects a line segment at a right angle.
perpendicular bisector:
A line, ray, or line segment that bisects a line segment at a right angle.
measure of each exterior angle =
360 ÷ n
transversal
A line, ray, or segment that intersects two or more coplanar lines, rays, or segments at different points.
Point C is between points A and B if AC+CB _______ AB
=
What symbols means parallel in diagrams?
>> Or II
linear pair
A pair of adjacent angles whose measures add up to 180°. _________ pairs of angles are supplementary.
semicircle:
A 180° arc; half of a circle.
polygon
A closed plane figure.
ratio
A comparison that shows the relative size of one quantity with respect to another. The ratio a to b is often written with a colon (a:b) or as a fraction ().
Definition
A definition is the precise statement of the qualities of an idea, object or process example. A donuts is a bagel with sugar on it usually and sometimes substances like jelly inside of it.
Venn diagram
A diagram that uses two or more circles or other shapes to represent sets. Elements that belong to more than one set are placed in the areas where the circles overlap.
plane
A flat surface that extends forever in all directions. A _________ has no thickness, so it has only two dimensions.
plane
A flat surface that extends forever in all directions. A _________has no thickness, so it has only two dimensions.
syllogism
A form of deductive reasoning that combines two or more related conditional statements in order to arrive at a conclusion. Example: If I open the door, then the cat will come in. If the cat comes in, then I will feed him. Therefore If I open the door, then I will feed the cat.
law of reflection
A law stating that the angle of incidence is congruent to the angle of reflection.
Triangle proportionality theorem
A line parallel to one side of triangle divides the other two sides proportionally.
median of a triangle
A line segment joining a vertex of a triangle to the midpoint of the opposite side.
Angle Bisector
A line segment that perfectly cuts an angle in half
angle bisector
A ray that divides an angle into two angles of equal measure.
in 10 words or fewer, what is special about the angels of a rectangle
A rectangle has four right angels
30-60-90 triangle
A right triangle with interior angle measures of 30°, 60°, and 90°. In a 30-60-90 triangle, the hypotenuse is always twice as long as the shorter leg and the longer leg is √3 times as long as the shorter leg
Pythagorean triple
A set of three whole numbers, a, b, and c, that satisfies the equation a2 + b2 = c2. . If the side lengths of a triangle form a __________________ , it is a right triangle.
converse
A statement in the form "If B, then A," given the statement "If A, then B."
inverse:
A statement in the form "If not A, then not B," given the statement "If A, then B."
contrapositive
A statement in the form "If not B, then not A," given the statement "If A, then B."
conjecture
A statement that appears to be correct based on observation but has not been proven or disproven.
conditional statement
A statement that has the form "If A, then B," where A is what you assume is true and B is the conclusion.
triangle congruence postulate:
A statement that proves triangles are congruent without requiring that the measures of all six pairs of corresponding parts be known..
congruence statement
A statement that tells which sides or angles of two triangles are congruent.
SAS similarity theorem:
A theorem stating that if an angle of one triangle is congruent to an angle of another triangle, and if the lengths of the sides including these angles are proportional, then the triangles are similar.
HL congruence theorem
A theorem stating that if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the right triangles are congruent
HA congruence theorem
A theorem stating that if the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle, then the right triangles are congruent.
LA congruence theorem
A theorem stating that if the leg and an acute angle of one right triangle are congruent to the leg and corresponding acute angle of another right triangle, then the triangles are congruent.
LL congruence theorem
A theorem stating that if the legs of one right triangle are congruent to the corresponding legs of another right triangle, then the right triangles are congruent.
SSS similarity theorem
A theorem stating that if the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.
AAS theorem
A theorem stating that if two angles and a nonincluded side of one triangle are congruent to the corresponding two angles and side of another, then the triangles are congruent.
isosceles triangle theorem
A theorem stating that if two sides of a triangle are congruent, then the angles opposite those sides are congruent.
right angle
An angle that measures 90°. ________ angles are often marked with a small square symbol.
isosceles trapezoid
A trapezoid with two congruent legs. The base angles of an isosceles trapezoid are also congruent.
acute triangle
A triangle in which all three interior angles are less than 90
scalene triangle
A triangle in which all three sides have different lengths.
right triangle
A triangle that contains a right angle
right triangle
A triangle that contains a right angle.
isosceles triangle:
A triangle that has at least two congruent sides. The angles opposite these sides are also congruent.
isosceles triangle
A triangle that has at least two congruent sides. The angles opposite these sides are also congruent. Note that an equilateral triangle is isosceles because it has more than two congruent sides.
obtuse triangle
A triangle that has one angle measuring more than 90°.
equilateral triangle
A triangle with three sides of equal length. The three angles of an ____________ each measure 60°.
Radian
A unit of angular measure determined by the condition: The central angle of one radian in a circle of radius 1 produces an arc of length 1.
deduction
A way of thinking that starts with a given set of rules and conditions and figures out what must be true based on what is given.
induction
A way of thinking that uses observations to form a general rule.
acute angle
An angle that measures less than 90°. An _____ angle is smaller than a right angle.
straight angle
An angle whose sides form a line.
______________ can not be used to find all side and angles lengths
AAA SSA
HA and LA (leg not included) are really just
AAS
LA (leg included) Is really just
ASA
Complementary
Adds up to 90
Alternate interior angles theorem
All Alternate interior angles are congruent
Properties specific to rectangles
All angles are right angles Diagonals are congruent
corresponding angles theorem
All pairs of corresponding angels are congruent.
Rhombus Properties
All sides are congruent Diagonals are perpendicular diagonals bisect opposite angles
CPCTC
An abbreviation that stands for "corresponding parts of congruent triangles are congruent." If two triangles are congruent, each side or angle of one triangle is congruent to the corresponding side or angle of the other triangle.,
congruence transformation
An action that can be performed on a geometric object without changing its size or shape.
zero angle
An angle that has a measure of zero degrees and whose sides overlap to form a ray.
45-45-90 triangle
An isosceles right triangle with interior angle measures of 45°, 45°, and 90°. In a 45-45-90 triangle, the two legs have the same length and the hypotenuse is √2 times as long as either leg.
Vertical angels
Angels that share a vertex and are congruent.
corresponding angles:
Angles that are in the same position
adjacent angles
Angles that share a vertex and one side.
What are the three ways to name an angle
By vertex and two other points. by vertex. and by a number
Two or more points are _________ if they lie on the same line
Collinear
vertical angles made by perpendicular lines are ___________
Congruent.
leg
Either of the two shorter sides of a right triangle.
Reflexive property.
Every Triangle is congruent to itself.
Symmetric Property
Every congruence statement can be reversed.
Ray
Has one endpoint and goes on forever in the other direction.
supplementary angles
Having angle measures that add up to 180°. If two ____________ angles are adjacent, they form a straight angle.
supplementary
Having angle measures that add up to 180°. If two ______________ angles are adjacent, they form a straight angle.
complementary angles
Having angle measures that add up to 90°. If two ____________ are adjacent, they form a right angle.
finite
Having boundaries
proportional
Having equal ratios..
similar
Having exactly the same shape. corresponding angles are congruent and corresponding sides are proportional in length.
two-dimensional
Having length and width but no height.,
one-dimensional
Having length but no width or height. Segments, Rays, Lines
three-dimensional
Having length, width, and height.
infinite
Having no boundary or limit. Lines, Rays
zero-dimensional
Having no length, width, or height. A point
congruent
Having the same size and shape.
congruent
Having the same size and shape. If polygons are ___________, their corresponding sides and angles are also _____________.
congruent
Having the same size and shape. If polygons are congruent, their corresponding sides and angles are also congruent. The symbol means "congruent."
A ______ is one dimensional and has infinite length
Line
parallel lines
Lines lying in the same plane without intersecting.
parallel lines
Lines lying in the same plane without intersecting. Two or more lines are _______ if they lie in the same plane and do not intersect.
skew lines
Lines that are not in the same plane. __________ do not intersect, and they are not parallel.
perpendicular lines
Lines that meet to form a right angle The symbol ⊥ means ____________________
collinear
Lying in a straight line. Two points are always ___________. Three or more points are ____________if a straight line can be drawn through all of them. Linear sounds like line
parallel
Lying in the same plane without intersecting. Two or more lines are ______________if they lie in the same plane and do not intersect.
coplanar
Lying in the same plane. Four or more points are _____________ if there is a plane that contains all of them.
Translation
Moving a shape
Does the theorem AAA work?
No
Does the theorem SSA work?
No.
Right circumcenter
On hypotenuse
vertex
One of the points at which the sides of a triangle meet.
All properties of a parallelogram
Opposite sides are parallel Opposite sides are congruent Opposite angles are congruent Consecutive angles are supplementary The diagonals bisect each other.
Obtuse Circumcenter
Outside
linear pairs
Pairs of adjacent angles whose measures add up to 180°. _________________ of angles are supplementary.
SSS step 1.
SSS: Find the cosine of the missing angel by using cos (c) = a² + b² -c² _______________________ 2ab
SSS Step 3.
SSS: Multiply arc cosine answer by 180/π
A ________ Is a zero dimensional geometric object.
Point
Segment Addition Postulate
Point C is between points A and B if AC + CB = AB
When are points not collinear?
Points are not collinear when they are scattered and cannot be connected with a single line. Also when there are more than two points.
Reflection
Reflect a shape
Rotation
Rotating a shape
SAS Step 1.
SAS: Draw a picture of a situation
SAS Step 3.
SAS: Plug all given information into the formula c= √ a² + b² -2abcos(c) (SOLVE IN CHUNKS THEN PLUG IN)
SAS Step 2.
SAS: if an object turned a certain amount of degrees subtract that from 180 to find the angel in the triangle.
_____________ can be used to find all side and angles lengths
SSS SAS SAA ASA
SSS Step 2.
SSS: Find inverse cosine of your answer. (Arccosine)
Parallel lines have the same?
Slope
Which of these objects are two-dimensional? Check all that apply. A. Point B. Segment C. Square D. Line E. Solid F. Plane
Square Plane
postulates
Statements that are assumed to be true without proof. They are also called axioms.
How do you find the sum of interior angels in a polygon?
Sum=(N-2) 180Degrees
How do you find the measure of each interior angel of a polygon?
Take the sum of the angel measures and divide by the number of sides.
angle of incidence
The angle between a ray of light meeting a surface and the line perpendicular to the surface at the point of contact.
angle of reflection
The angle between a ray of light reflecting off a surface and the line perpendicular to the surface at the point of contact.
angle of reflection
The angle between a ray of light reflecting off a surface and the line perpendicular to the surface at the point of contact..
secant-secant angle
The angle formed by the intersection of two secants of the same circle. The measure of a secant-secant angle is half the difference of the measures of the intercepted arcs.
Describe how the area of a full circle compares to the area of slives of that circle.
The areas of the slices together form the area of the entire circle.
incenter
The center of the circle that can be inscribed in a given triangle. the point where the 3 angle bisectors intersect.
circumcenter of a triangle
The center of the only circle that can be circumscribed about a given triangle.the point shared by the perpendicular bisectors of the triangle's sides.
Circumcenter
The circumcenter of a polygon is the center of the circumscribed circle.
angles
The corner-like spaces where the sides of a triangle meet.
what is special about the diagonals of an isosceles trapezoid?
The diagonals of an isosceles trapezoid have equal lengths. In other words, the diagonals are congruent.
Longest Side and Largest Angle Theorem
The longest side of a triangle is always opposite the angle with the largest measure.
secant-secant theorem
The measure of a secant-secant angle is one-half of the difference between the two intercepted arcs..
angle
The object formed by two rays that share the same endpoint..
End point
The point at the very end of a ray or line.
orthocenter
The point at which the three altitudes of a triangle intersect. The _______________________ always falls inside an acute triangle and outside an obtuse triangle. For right triangles, the ____________ lies at the vertex of the right angle.
centroid
The point at which the three medians of a triangle intersect. The centroid of any triangle is inside the triangle..
Midpoint
The point in the very center of a line segment. They separate a line segment into two equal line segments.
vertices
The points at which the sides of a triangle meet.,
symmetry
The property of having a line, or axis, that divides a given shape into two identical parts.
scale factor
The ratio of the lengths of corresponding sides in similar figures. In a dilation, this is the factor by which the original figure is multiplied.
Line
The set of all points in a plane that are equidistant from two points.
hypotenuse
The side across from the right angle in a right triangle. It is the triangle's longest side.
Pythagorean theorem
The theorem that relates the side lengths of a right triangle. The theorem states that the square of the hypotenuse equals the sum of the squares of the legs: a2 + b2 = c2
sides
The three line segments that form a triangle
sides
The three line segments that form a triangle.
dilate
To change the size but not the shape of a geometric figure.
intersect
To cross over
Non Rigid transformations
Transformations that change lengths, and angles.
Transformation
Translation, Rotation, Reflection
similar triangles
Triangles that have exactly the same shape. Their corresponding angles are congruent, and their corresponding sides are proportional in length.
True or false? Any two points are collinear and coplanar.
True
alternate interior angles
Two angles formed by a line (called a transversal) that intersects two parallel lines. The angles are on opposite sides of the transversal and inside the parallel lines.
consecutive interior angles
Two angles formed by a line (called a transversal) that intersects two parallel lines. The angles are on the same side of the transversal and are inside the parallel lines.
What happens when you combine two rays?
You get a line.
When you make all the consecutive angels supplementary the quadrilateral turns into
a parallelogram
Pythagorean theorem
a2 + b2 = c2 A and B = leg C= hypotenuse
What is special about the side lenghts of a rhombus?
all four sides of a rhombus have equal side lengths
Midsegments
are segments connecting the two midpoints of separate sides of a triangle. As it turns out, they are also always parallel to the third side and half of that side's length.
what is special about the pairs of base angels in a isosceles trapezoid?
both pairs of base angles in an isosceles trapezoid are congruent.
Which law of cosines formula do you use when you know a side an angle and a side?
c= √ a² + b² -2abcos(c)
Three points are collinear if they
fall on the same line.
Hashmarks are?
lines that point out whither things are congruent.
Triangle with the same median and altitude
if a line dividing a triangle is both its altitude and its median, the triangle is an isosceles triangle.
The perpendicular bisector theorem
if a point is on the __________________ of a segment, then it is equidistant from the endpoints of the segment.
The angle bisector theorem
if a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
What does the symbol II mean?
parallel
When you make the Diagonals bisect each other, the quadrilateral becomes a
parallelogram. DIAGONALS
A____ Has no length, width or height
point
If the opposite angles of a quadrilateral are congruent, then the ___________________
quadrilateral is a parallelogram.
when you cross multiply two equal__________, the products are equal.
ratios
Perpendicular lines form _______ angles.
right
what is special about the angels of a parallelogram?
the angels of the opposite sides are equal.
what is special about diagonals in a parallelogram?
the diagonals intersect at the midpoint of each diagonal. they bisect each other.
What is the ratio of the hypotenuse of a 45-45-90 triangle?
the hypotenuse of a 45-45-90 triangle will always be x√2
what is special about an isosceles trapezoids legs?
the legs are congruent.
what is the relationship between the lengths of the median and the lengths of the bases?
the length of the median is always between the lengths of the bases.
What is special about the lengths of the sides of a parallelogram?
the lengths of the opposite sides are equal.
what is special about consecutive angels in a parallelogram?
the measure of consecutive angels always adds up to 180 degrees
When two adjacent sides of a parallelogram have the same length___________________________________________________________________________________
the shape becomes a rhombus
Shortest Side and Smallest Angle Theorem
the shortest side of a triangle is always opposite the angle with the smallest measure.
Triangle Inequality theorem
the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
How do you find the sum of the measures of exterior angels of a polygon?
the sum of the measures of the exterior angles of a polygon always equals 360 degrees
What special traits do rhombi have?
their diagonals form perpendicular bisectors. It is also a angle bisector.
What is always true about the diagonals of a rectangle?
they are always congruent.
What is special about the lengths of parallel sides in a parallelogram?
they are congruent
how can you find the length of an arc using the circumference of a circle and the fraction of the circle covered by the arc?
to find arc length, multiply the cirumference of the circle by the fraction covered by the arc. (devide by fraction)
Point
used to mark, and represent locations, they have no width, Height or length. They are labeled with capital letters
vertical angles theorem
vertical angles are congruent.
angle addition postulate
when point c is inside <AVB, m<AVC + m<CVB = m<AVB
Isosceles Triangle Property
whenever the measure of an exterior angle is exactly double the measure of one of its remote interior angles, the triangle is isosceles.
When you make both pairs of opposite angels congruent, does the quadrilateral become a parallelogram?
yes it makes a parallelogram
