Term
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Definition
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Term
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Definition
Represents location or position and is noted by a dot and an uppercase letter. It has
no length, width or thickness. |
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Term
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Definition
A set of points.
Notation: AB |
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Term
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Definition
Set of points that form a flat surface extending indefinitely in all directions.
3 points that are not on the same line will form a plane.
Ex: Surface of a floor, desk top, sheet of paper. |
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Term
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Definition
| Set of points which lie on the same straight line. |
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Term
| Non-collinear set of points |
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Definition
Set of three or more points that do not all lie on the same straight
line. |
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Term
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Definition
Set of points consisting of two points called endpoints and all of the points
in between the two endpoints.
Notation: AB |
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Term
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Definition
| (of a line segment) is the distance between the two endpoints. |
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Term
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Definition
Segments that have the same measure.
Symbol is ≅ .
Ex: AB CD |
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Term
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Definition
Point on the line segment that divides the segment into two congruent
segments. |
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Term
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Definition
(of a line segment) Any line or line segment that intersects the given line
segment at its midpoint. |
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Term
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Definition
Part of a line that consists of a point on the line (endpoint) and all points extending in
one direction. |
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Term
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Definition
Union of two rays that share an endpoint
Notation: ∠ABC
Note: The vertex of the angle must be the middle letter. |
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Term
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Definition
Angle that measures 180 degrees.
Looks like a straight line. |
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Term
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Definition
| Angle whose measure is greater than 0, but less than 90 degrees. |
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Term
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Definition
| An angle whose degree measure equals 90 degrees. |
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Term
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Definition
An angle whose degree measure is greater than 90 degrees, but less than
180 degrees. |
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Term
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Definition
| A ray that divides an angle into two congruent angles |
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Term
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Definition
Two lines that intersect to form right angles.
Ex: AB CD |
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Term
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Definition
A triangle that has no congruent sides.
So no congruent angles either! |
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Term
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Definition
A triangle that has 2 congruent sides.
So 2 congruent angles too! |
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Term
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Definition
A triangle that has 3 congruent sides.
So all 3 angles are congruent (60°) |
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Term
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Definition
| A triangle with three acute angles. |
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Term
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Definition
| A triangle with one right angle. |
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Term
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Definition
| A triangle with one obtuse angle. |
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Term
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Definition
A vertex is opposite a side in a triangle if it does not share an endpoint
with that side.
Ex: ∠C is opposite AB (not A or B) |
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Term
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Definition
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Term
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Definition
The opposite truth value of a given statement.
Symbol: ~ |
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Term
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Definition
Compound statement formed by combining two statements with the word
“AND”. Result is true if both parts are true.
Symbol: ∧
Rule: T ∧ = T T |
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Term
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Definition
Compound statement formed by combining two statements with the word
“OR”. Result is false if both parts are false.
Symbol: ∨
Rule: F F ∨ = F |
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Term
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Definition
Compound statement formed by combining two statements with the
phrase if . . . then. Result is false if the first part is true and the second
part is false.
Symbol: →
Rule: T → = F |
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Term
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Definition
First statement in a conditional statement.
It follows the word “if”. |
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Term
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Definition
Second statement in a conditional statement.
If follows the word “then”. |
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Term
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Definition
A statement formed by negating the hypothesis and the conclusion in a
conditional statement.
Original: A → Inverse: ~ A → ~ B |
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Term
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Definition
A statement formed by swapping the hypothesis and the conclusion in a
conditional. (Changing order)
Original: A →B Converse: B →A |
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Term
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Definition
Statement formed by performing the inverse and the converse to a
conditional statement.
Original: A → B Contrapositive: ~ B → ~ A |
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Term
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Definition
Compound statement formed by combining a conditional statement and its
converse with the word “and”.
Usually written with the words “if and only if”.
Result is true if both truth values are equal.
Symbol: ↔
Rule: T ↔ = T T , F F ↔ = T |
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Term
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Definition
Line segment drawn from any vertex in a triangle to the opposite side and it is
perpendicular to the opposite side.
AD is the altitude
from A to BC |
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Term
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Definition
Line segment drawn from any vertex to the midpoint of the opposite side.
BZ is the median from B to AC |
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Term
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Definition
Line segment whose endpoint bisects any angle of a triangle and the other
endpoint is on the opposite side of the angle.
Ex: BZ is the angle bisector from
B to AC |
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Term
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Definition
A line (or line segment) that is perpendicular to the line segment and
intersects its midpoint.
Ex: YZ is the perpendicular bisector
of A |
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Term
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Definition
Two adjacent (attached) angles that form a straight angle (straight line).
Ex: ∠ABD and ∠DBC are a linear pair
(∠ + ∠ = ABD DBC 180°) |
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Term
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Definition
Two congruent angles formed by intersecting lines – they share the same
vertex, but opposite rays.
Ex: AC and BD
HJJG HJJG
intersect,
∠1 and ∠2 are vertical angles
∠1 ≅ ∠ 2 |
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Term
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Definition
Two angles that share a vertex and a common side.
Ex: ∠ABC and ∠CBD are adjacent angles.
Shared vertex = B
Shared side = Bc |
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Term
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Definition
| Two angles whose sum is 90°. They form a right angle. |
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Term
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Definition
| Two angles whose sum is 180°. They form a straight angle. |
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Term
Exterior Angle of a
Polygon |
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Definition
An angle that forms a linear pair with one of the interior angles of a
polygon.
Ex: ∠BCD is an exterior angle to ΔABC
(∠ACB and ∠BCD are a linear pair) |
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Term
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Definition
The sum of any two sides of a triangle MUST be greater than the third
side.
Ex: a + b > c
b + c > a
a + c > b |
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Term
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Definition
The sum of any two interior angles of a triangle is equivalent to the
exterior angle of the third angle.
Ex: Given ΔABC
1 2 = ∠5 (outside ∠3)
∠ + ∠ = ∠ 2 3 4 (outside ∠1 )
∠ + ∠ = ∠ 1 3 6 (outside ∠2 ) |
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Term
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Definition
| Rate of change of the y-values compared to the x-values of two points. |
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Term
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Definition
y = mx + b
m = slope
b = y-intercept
(x, y) = any point on the line |
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Term
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Definition
| Used to find the equation of a line. |
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Term
Finding Equation of
a Line |
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Definition
• Use Equation of a line (#51) – need a point and a slope
Plug in your point (x, y) and slope (m) into y = mx + b
Solve for b.
Rewrite y = mx + b, using your slope (m) and your b (just solved)
• Use Point-slope formula (#52) |
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Term
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Definition
A point that divides a line segment into 2 congruent segments.
It is the average of the two points |
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Term
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Definition
Two or more line who do not intersect.
Parallel lines have equal slopes. |
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Term
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Definition
Two lines who intersect and form right angles.
Perpendicular lines have negative reciprocal slopes |
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Term
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Definition
| Distance is the length between two points. |
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Term
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Definition
| Three or more lines that intersect at one point. |
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Term
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Definition
The point of intersection of the three medians in a triangle.
The three medians intersect at centroid P.
• Can be calculated by graphing or
by finding the average of the 3 vertices |
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Term
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Definition
The point of intersection of the three altitudes of a triangle.
• If the triangle is obtuse, the orthocenter will be outside the triangle.
• Can only be calculated by graphing |
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Term
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Definition
The point of intersection of the three angle bisectors of a triangle.
(It is the center of a circle that is inscribed inside the triangle.) |
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Term
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Definition
The point of intersection of the three perpendicular bisectors of a triangle.
(It is the center of a circle that is circumscribed about the triangle.)
• If the triangle is obtuse, the circumcenter will be outside the triangle |
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Term
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Definition
A line that intersects two parallel lines at two different points.
Ex: a b&
line t is the transversal |
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Term
Alternate Interior
Angles |
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Definition
Congruent angles formed by two parallel lines cut by a transversal.
• Alternate – opposite sides of the transversal.
• Interior – inside the two parallel lines
• Creates a Z shape |
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Term
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Definition
Congruent angles formed by two parallel lines cut by a transversal.
• Angle is in the same location from one parallel line to another.
• Creates an F shape. |
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Term
Same-side Interior
Angles |
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Definition
Supplementary angles formed by two parallel lines cut by a transversal.
• Same side – same side of the transversal.
• Interior – inside the two parallel lines
• Creates a C shape. |
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Term
| Sum of the Interior Angles of a Polygon |
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Definition
n = number of sides of the polygon
Sum (Interior) = 180(n – 2) |
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Term
| Sum of the Exterior Angles of a Polygon |
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Definition
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Term
| Each Interior Angle of a Polygon |
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Definition
| each mesurment of an interior angle |
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Term
| Each Exterior Angle of a Polygon |
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Definition
| each mesurment of an exterior angle |
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Term
| Find number of sides in a Polygon: |
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Definition
Number of sides = 360/
Exterior Angle |
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Term
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Definition
| A polygon with all sides congruent and all angles congruent |
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Term
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Definition
Triangle – 3 sides
Quadrilateral – 4 sides
Pentagon – 5 sides
Hexagon – 6 sides
Octagon – 8 sides
Decagon – 10 sides |
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Term
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Definition
Quadrilateral with two pairs of opposite sides parallel.
• Opposite sides congruent
• Opposite angles congruent
• Consecutive angles supplementary
• Diagonals bisect each other |
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Term
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Definition
Parallelogram with consecutive sides perpendicular.
• All properties of a parallelogram
• Diagonals are congruent
(because sides perpendicular) |
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Term
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Definition
Parallelogram with all sides congruent.
• All properties of a parallelogram.
• Diagonals are perpendicular
(because sides are congruent)
** Draw like a kite with 4 identical right triangles! |
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Term
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Definition
Parallelogram with consecutive sides perpendicular (like rectangle) and all
sides congruent (like rhombus) |
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Term
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Definition
Quadrilateral with only one pair of opposite sides parallel.
The parallel sides are called the bases |
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Term
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Definition
Trapezoid where the non-parallel sides (legs)
are congruent |
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Term
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Definition
The mean proportional of two numbers (a and b) is x in the following
proportion |
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Term
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Definition
All the angles in one polygon are congruent to all the angles in another
polygon.
• Corresponding sides are in proportion. |
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Term
Similar Polygons and
Line Segments |
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Definition
If two polygons are similar, the corresponding altitudes, medians and
angle bisectors will have the same ratio as any of the two
corresponding sides. |
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Term
Similar Polygons and
Perimeter |
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Definition
If two polygons are similar, then the ratio of the corresponding
perimeters is equal to the ratio of any two corresponding sides. |
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Term
Similar Polygons and
Area |
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Definition
If two polygons are similar, then the ratio of the corresponding areas is
equal to the square of the ratio of any two corresponding sides |
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Term
Similar Polygons and
Volume |
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Definition
If two polygons are similar, then the ratio of the corresponding
volumes is equal to the cube of the ratio of any two corresponding
side |
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Term
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Definition
| The relationship of the three sides of a right triangle. |
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Term
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Definition
| Any set of three integers that can be the sides of a right triangle |
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Term
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Definition
Most common integer solutions (and their multiples)
3, 4, 5 7, 24, 25
5, 12, 13 8, 15, 17 |
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Term
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Definition
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Term
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Definition
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Term
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Definition
Set of all points in a plane that are equidistant (radius) from a fixed point called a
center. |
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Term
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Definition
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Term
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Definition
Angle whose vertex is the center of the circle.
In circle O, is a central angle and
intercepts
∠LOM
LMp .
∠MOR is a central angle and intercepts MRp. |
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Term
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Definition
Part of a circle between any two points on the
circle |
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Term
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Definition
Arc that is the shortest distance between any two
points on a circle |
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Term
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Definition
| Arc that is the longest distance between any two points on a circle. |
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Term
Measure of a
Central Angle |
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Definition
| Central Angle = Measure of the Intercepted Arc |
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Term
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Definition
An angle whose vertex is on the circle and the
endpoints of both sides are also on the circle |
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Term
Measure of an
Inscribed Angle |
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Definition
| Inscribed Angle =1/2 (Measure of Intercepted Arc) |
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Term
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Definition
| Line segment whose endpoints are points on the circle |
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Term
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Definition
| Chord that passes through the center of the circle. |
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Term
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Definition
Line (or line segment) that intersects the
circle in one and only one point |
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Term
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Definition
Line (or line segment) that intersects the circle in two points.
Line k is secant to circle O at points A and B |
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Term
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Definition
Two tangents segments drawn to a circle from the same point are
congruent |
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Term
Angles formed by
Tangents |
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Definition
A tangent segment to a circle is perpendicular to all radii or diameter that
intersect the point of tangency |
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Term
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Definition
An angle formed by two chords which lies
in the interior of the circle |
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Term
Measure of
Interior Angles |
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Definition
| Interior Angle =1/2( Sum of Intercepted Arcs) |
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Term
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Definition
An angle formed by two tangents, two secants or one secant and one
tangent. It lies outside the the circle.
Ex: The three different ways that exterior angle P can be respresented. |
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Term
| measure of exterior angles |
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Definition
| Exterior Angle =1/2 (Difference of Intercepted Arcs) |
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Term
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Definition
| If two chords intersect,then the product of the segments of one chord is equal to the product of the segments of the second chord. |
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Term
Measure of
Secants/Tangents |
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Definition
if there are two secants or one tangent and one secant, then the products
of the exterior segment and the entire segment of each secant and/or
tangent are equal |
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