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Midterms
review
50
Mathematics
10th Grade
01/21/2015
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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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