Alternate interior angles |
Alternate Interior
Angles are
a pair of angles formed by two lines and a transversal and are located on
opposite sides of the transversals and inside or between (on the interior of)
the two lines. Ð3 & Ð5 and Ð4 & Ð6 are alternate interior
angles. Theorem: If the lines are
parallel, alternate interior angles are congruent. Ð3 @ Ð5 and Ð4 @ Ð6 |
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Alternate exterior angles |
Alternate exterior
angles
are a pair of angles formed by two lines and a transversal and are located on
opposite sides of the transversals and outside (on the exterior of) the two
lines. Ð1 & Ð7 and Ð2 & Ð8 are alternate interior
angles. Theorem: If the lines are parallel,
alternate exterior angles are congruent. Ð1 @ Ð7 and Ð2 @ Ð8 |
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Area |
The number of square units that cover a shape or
surface. |
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Arrow diagram |
A diagram using arrows to show logical connections. An arrow
diagram can be used in place of an ‘if, then’ statement: ‘If P, then Q’ is equivalent to ‘P à Q’ |
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Base |
A side of a polygon. The base is the side perpendicular to the
height of the polygon. In a trapezoid,
the bases are the two parallel sides. |
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Complementary angles |
Any two angles whose measures add to 90 degrees. |
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Conditional statement |
A statement in the form, ‘If P, then Q’ where P is the
hypothesis and Q is the conclusion. |
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Conjecture |
A statement that has not been proved. |
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Corresponding angles |
Corresponding angles are a pair of angles
formed by two lines and a transversal and are located in the same quadrant
formed by the intersection of the transversal and one of the lines. Ð1 & Ð5, Ð2 & Ð6, Ð3 & Ð7, and Ð4 & Ð8 are corresponding
angles. Postulate: If the lines are
parallel, corresponding angles are congruent. Ð1 @ Ð5 Ð2 @ Ð6 Ð3 @ Ð7 Ð4 @ Ð8 |
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Dimensions |
The measurements of the lengths of the
sides, base, altitude, height, radius, circumference, perimeter, apothem, angles,
slant heights, and any other parts of a shape. |
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Height |
The altitude, or perpendicular segment from
a vertex to the line containing the opposite side, or base, of a polygon. |
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Hypotenuse |
The longest side of a right triangle. The side of a triangle that is opposite the right angle. |
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Leg |
The sides forming the right angle in a right triangle. The
non-parallel sides of a trapezoid. The two congruent sides of an isosceles
triangle. |
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Line |
A line is straight, infinitely long, and has no width. |
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Parallelogram |
A quadrilateral with two pair of parallel sides. A quadrilateral whose diagonals bisect each other. A quadrilateral with two pairs of congruent opposite sides. |
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Perimeter |
The distance around a shape. |
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Proof by contradiction |
To assume the reverse of what is to be proved, show it is
impossible by contradicting a known fact, thus proving that the opposite must
be true. |
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Pythagorean Theorem |
In a right triangle, the sum of the squares of the legs equals
the square of the hypotenuse. |
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Rectangle |
The geometric shape: A quadrilateral with 4 right angles. A quadrilateral with congruent diagonals that bisect each other. A quadrilateral with 2 pairs of parallel sides and a right
angle. A parallelogram with a right angle. A parallelogram with congruent diagonals. |
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Right angle |
An angle with measure 90 degrees. |
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Same-side interior angles |
Same-side interior
angles
are a pair of angles formed by two lines and a transversal and are located on
the same side of the transversals and between (on the interior of) the two
lines. Ð3 & Ð6 and Ð4 & Ð5 are same-side interior
angles.
t Theorem: If the lines are
parallel, same side interior angles are supplementary. Ð4 and Ð5 are supplementary. Ð3 and Ð6 are supplementary. |
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Square |
The geometric shape: A quadrilateral with 4 congruent sides and 4 right angles. A rectangle with 2 adjacent congruent sides. A parallelogram with a right angle and 2 adjacent congruent
sides. A rhombus with a right angle. A parallelogram with diagonals that are perpendicular and
congruent. The numerical value: A number that is the product of two identical real numbers. (3)(3) = 9, so 9 is the square of 3. The square of the side of a square gives the Area of the square. |
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Square root |
The number, when multiplied by itself, that equals a given
number is called the square root of that number. (3)(3) = 9, so 3 is the square root of 9. The square root of the area of a square gives the length of the
side of the square. |
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Straight angle |
Definition: A straight angle is an angle whose sides form a line and whose
measure is 180°. ÐAVC is a straight angle. mÐAVC = 180° Definition: A straight angle pair is two angles adjacent angles whose
exterior sides form a straight line. Ð1 and Ð2 are a straight angle
pair. Theorem: The sum of the measures
of a straight angle pair equals 180°. mÐ1 + mÐ2 = 180° Theorem: A straight angle pair
is supplementary. |
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Supplementary
angles |
Supplementary
angles are any two angles whose measures add to 180°. |
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Theorem |
A
statement that has been proved using logic, deductive reasoning, postulates,
definitions, and previously proved theorems, and rules of algebra. |
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Transversal |
A line that intersects two other lines in two distinct points.
Line t is the transversal of lines m and n. |
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Trapezoid |
A quadrilateral with exactly one pair of parallel sides. |
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Triangle Inequality Theorem |
In a triangle, the third side of the triangle is greater than
the difference of the other two sides and at the same time is less than the
sum of the other two sides. |a – b| < c < a + b for a, b, c sides of a triangle. |
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Unit of measure |
A defined length, such as 1 inch or 1 kilometer, that is used to
measure the distance between two points. |
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Vertical angles |
Definition: Vertical angles are formed by two intersecting lines. Vertical angles share a common vertex but
no common sides. Ð1 and Ð3 are vertical angles. Ð2 and Ð4 are vertical angles Theorem: Vertical angles are
congruent. Ð1 @ Ð3 Ð2 @ Ð4 |