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28 Cards in this Set

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midpoint
halfway

if section length is known, can divide by 2 to get the length from one end to the midpoint
sum of interior angles of a triangle
180 degrees
measure of an exterior angle of a triangle
the sum of the measures of the remote interior angles of the triangle
sum of exterior angles of any triangle
360 degrees
area of a triangle
1/2(base)(height)
triangle inequality theorem
Each side of a triangle is greater than the difference and less than the sum of the other two sides.
similar triangles
triangles that have the same shape: corresponding angles are equal, corresponding sides are proportional
isosceles triangles
a triangle that has two equal sides, angles opposite the equal sides are equal
equilateral triangle
a triangle that has three equal sides. All angles are also equal, all 60 degrees.

Area of an equilateral triangle = (s^2 x sqrt[3])/4
right triangle
a triangle with a 90 degree angle. Sides that form the right angle are called legs.

Area of a right triangle = 1/2(leg 1)(leg2)
Pythagorean theorem
for right triangles

(leg1)^2 + (leg2)^2 = (hypotenuse)^2
Pythagorean triplet
a set of integers that fits the Pythagorean theorem

3:4:5
3-4-5 triangle
if a right triangle's leg ratio is 3:4, or if the leg-hypotenuse ratio is 3:5 or 4:5, then it is a 3-4-5 triangle, so the Pythagorean theorem is not needed to find the missing side.
5-12-13 triangles
another Pythagorean triplet right triangle. Just figure out what multiple of 5-12-13 it is to find the missing side.
45 degree-45 degree-90 degree triangle
side of this right triangle are in a ratio of 1:1:sqrt(2)
30-60-90 degree triangles
right triangle whose sides are in a ratio of 1:sqrt(3):2
hidden special triangles
sometimes adding a line segment to a shape can create special triangles for you to use to solve the problem

dropping altitudes and perpendiculars are often very useful
special quadrilaterals
trapezoids, parallelograms, rectangles, rhombus, square
trapezoid
4 sided figure with one pair of parallel sides and one pair of non parallel sides

area= [(base1+base2)/2]x height
parallelograms
4-sided figure, two pairs of parallel sides. Opposite sides are equal, opposite angles are equal.

area= base x height
rectangle
4-sided figure with 4 right angles
opposite sides are equal
perimeter is equal to the sum of the 4 sides
area=length x width
rhombus
4-sided figure with 4 equal sides

area=base x height
square
4 sided figure with four right angles and four equal sides

area=(side)^2
hexagon
6 equal sides

area = [3s^2sqrt(3)]/2
circumference
perimeter of a circle

2(pi)r or (pi)d
length of an arc
piece of a circumference

(n/360)(2 pi r)

n=degree of arc's central angle
area of a circle
pi r^2
area of a sector
sector - piece of the area of a circle

(n/360)(pi r^2)