# Shared Flashcard Set

## Details

Midterms
review
50
Mathematics
01/21/2015

Term
 Distance formula for a coordinate plane:
Definition
 d=√(x2-x1)²+(y2-y1)²
Term
 Pythagorean Theorem:
Definition
 a²+b²=c²
Term
 Midpoint Formula:
Definition
 (x1+x2 over 2, y1+y2 over 2)
Term
 Complementary angles:
Definition
 2 angles that add up to 90°
Term
 Supplementary angles:
Definition
 2 angles that add up to 180°
Term
 Regular:
Definition
 all angles and sides are congruent
Term
 Perimeter for a circle:
Definition
 C=2∏r
Term
 Area for a triangle:
Definition
 A=½•base•height
Term
 Area for a circle:
Definition
 A=∏r²
Term
 Conjunction:
Definition
 join 2 statements using "and"
Term
 Disjunction:
Definition
 join 2 statements using "and" true if one or the other or both are true
Term
 Hypothesis(p):
Definition
 "if"
Term
 Conclusion(q):
Definition
 "then"
Term
 Converse: q→p
Definition
 reverses the hypothesis and conclusion
Term
 Inverse: ~p→~q
Definition
 negates the hypothesis and conclusion
Term
 Contrapositive: ~q→~p
Definition
 negates and reverses the hypothesis and conclusion
Term
 Bioconditional: p↔q
Definition
 an if and only if statement (iff)
Term
 Law of Detachment:
Definition
 if a conditional is true and the "if" part is true, we conclude the "then" part is true
Term
 Law of Syllogism:
Definition
 p→q , and q→r, then p→r
Term
 Alternate interior angles:
Definition
 2 angles that are nonadjacent, interior, and on opposite sides of the transversal
Term
 Alternate exterior angles:
Definition
 nonadjacent, outside the lines, and on opposite sides of the transversal
Term
 Same-side interior angles:
Definition
 nonadjacent, interior, same side of the transversal
Term
 Same-side exterior angles:
Definition
 nonadjacent, exterior, same side of the transversal
Term
 Corresponding angles:
Definition
 nonadjacent, same side of the transversal, and both above the lines, or both below the lines
Term
 Standard slope equation: slope: -A/B
Definition
 Ax+By=C
Term
 Slope-intercept equation: slope: m
Definition
 y=mx+b
Term
 Point-slope equation: slope: m
Definition
 y-y1=m(x-x1)
Term
 Horizontal slope equation:slope: 0
Definition
 y=#/y=b
Term
 Vertical slope equation: slope: undefined
Definition
 x=#/x=a
Term
 Triangle angle sum theorem:
Definition
 The sum of the 3 angles in a triangle is 180°
Term
 Hypotenuse-Leg Theorem:
Definition
 If the hypotenuse and leg of one right triangle is congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.
Term
 Ratio:
Definition
 comparison of the size of 2 items
Term
 Extended ratio:
Definition
 compare 3 or more items
Term
 Proportion:
Definition
 equation w/2 ratios set equal
Term
 Notation for proportions:
Definition
 a  =  b means  --      --                 c  =  d extremes
Term
 Angle bisector:
Definition
 ray/segment that divides an angle into 2 congruent angles
Term
 Altitude:
Definition
 segment from a vertex, perpendicular to the opposite side
Term
 Median:
Definition
 segment from a vertex to the midpoint of the opposite side
Term
 Scale ratio:
Definition
 map length ------------- actual distance or model ------------- actual size
Term
 Concurrent lines:
Definition
 3 or more lines that intersect in a single point
Term
 Point of concurrency:
Definition
 The point where 3 or more likes intersect
Term
 Circumcenter:
Definition
 center of the circumscribed circle -point of concurrency at the perpendicular bisectors of the triangle
Term
 Incenter:
Definition
 center of the inscribed circle -point of concurrency of the angle bisectors
Term
 Median of a triangle:
Definition
 A segment from a vertex to the midpoint of the opposite side
Term
 Centroid:
Definition
 the point of concurrency of the 3 medians of a triangle *center of gravity of the triangle*
Term
 Altitude:
Definition
 segment from a vertex to a line containing the opposite side and meeting at a right angle
Term
 Orthocenter:
Definition
 point of concurrency of the altitudes of a triangle
Term
 Triangle Exterior Angle Theorem:
Definition
 The measure of an exterior angle is greater than the measures of its remote interior angles.
Term
 Triangle Angle/Side Relationships
Definition
 •If 2 sides of a triangle are not congruent, then the longer side is across from the larger angle •If 2 angles of a triangle are not congruent, then the larger angle is across from the larger side.
Term
 Hinge theorem:
Definition
 If 2 sides of one triangle are congruent to two sides of another triange, but the included angles are different, then the triangle with the larger included angle has a larger 3rd side
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