 | Term | Definition |
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Inductive reasoning |
based on a pattern |
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Conjecture |
educated guess coming from inductive reasoning |
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Counter example |
Disproving conjecture |
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Deductive Reasoning |
Using logic to draw conclusions from given facts |
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Theorem |
Any statement you can prove |
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Alternate exterior angles |
Angles that lie on the opposite side of the transversal outside the parallel lines |
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Alternate interior angles |
Non-adjacent angles that lie on opposite sides of the transveral between the lines |
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Same-side interior angles |
Angles that lie on the same side of the transversal between the parallel lines |
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Corresponding Angles |
Angles that lie on opposite sides of the transveral (aaah idk!) |
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Transversal |
A line that intersects two parallel coplanar lines |
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Parallel lines |
Coplanar lines that never intersect |
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Parallel planes |
planes that never interect |
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Perpendicular bisector |
a line perpendicular to a segment at the it's midpoint |
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Point slope form |
y-y=m(x-x) |
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Rise |
the difference in the y values on 2 points on the line |
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Run |
the difference in the x values on 2points on the line |
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Skew lines |
lines that are not parallel but never intersect |
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Slope |
the ratio of rise to run (y-y) over (x-x) equation: y1 - y2 ove x1 - x2 |
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Slope intercept form |
y=mx+b |
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Triangle Sum theorem |
The sum of all the angle measures of a triangle is 180 degrees |
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Acute angles of a right triangle |
The acute angles of a right triangle that are complimentary |
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Equilateral Triangle |
When all the angle measures in an equalateral triangle are 60 degrees |
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Exterior angles |
the measure of an exterior angle of a triangle is equal to the sum of the measures of its remote intirior angles |
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Interior |
the set of all inside points |
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Acute Triangles |
All angles are less than 60 degrees |
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CPCTC |
Corresponding parts of congruent triangles are congruent |
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Isosceles Triangle |
two sides and two angles of a triangle are congruent |
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Auxiliary lines |
a line that is added in aid of a proof |
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Equiangular Triangle |
All the angles are congruent |
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Legs of an isosceles |
congruent sides in a isosceles triangle |
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Base |
bottom of a triangle |
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Obtuse triangle |
One of the angles in a triangle is larger than 90 degrees |
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Right Triangle |
One of the angles on a triangle is equal to 90 |
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Right angle |
An angle that is exactly 90 degrees |
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Coordinate Proof |
A style of proof that uses geometry and algebra |
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Included Angle |
An angle created by two adjacent sides |
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Scalene Triangle |
All the measures of the sides are different |
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Corollary |
The theorem that follows right after another theorem |
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Included side |
A common side of two executive angles |
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Triangle Rigidity |
If the side lengths are given there is only one specific shape |
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Corresponding angles |
Angles that are congruent |
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Vertex |
The angle formed by two legs |
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Corresponding sides |
sides that are congruent |
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Interior angle |
An inside angle |
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Exterior angle |
An outside angle |
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Remote intirior angle |
An interior angle that is not adjacent to the extirior angle |
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two angles |
If two angles of one triangle are congruent to two angles of another triangle then the 3rd angles is congruent |
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Parallel sides Theorem |
If 2 lines have the same slope than there parallel. |
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Perpendicular Lines Theorem |
in a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is -1. Verical and horisantal lines are perpendicular |
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Corresponding angles Postulate |
If two parallel lines are cut by a transversal then the pairs of corresponding angles are congruent. |
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Alternate Extirior angles theorem |
if two parallel lines are but by a transversal then the alternate interior lines angles are congruent. |
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Same side intirior angles |
if two parallel lines are but by a transversal then the same side interior angles are supplementary. |
