sum of interior angles of a polygon
180(n-2) (n being the number of sides)
each interior angle of a regular polygon.
180(n-2)/n (n being the number of sides)
sum of exterior angles of a polygon
360
each exterior angle of a regular polygon
360/n (n being the number of sides)
scalene triangle
no congruent sides
isosceles triangle
2 congruent sides
equaliteral triangle
3 congruent sides
actue angle
angles < 90
right angle
an angle that measures 90 degrees
obtuse angle
angle > 90
equiangular angle
3 congruent angles (60)
triangles
180 degrees
exterior angle theorem
the exterior angle is equal to the sum of the two non-adjacent interior angles
midsegment
a segment connecting the midpoints of two sides of a triangle, 1/2 the length of the third side, spilts the triangle into 2 similar triangles, always parallel to the third side
slope-intercept form of a line
y=mx+b (m is the slope, b is the y intercept point)
point slope form of a line
y - y1 = m (x - x1); where (x1, y1) is a point on the line
slope formula
y2 - y1/x2 - x1
positive slope
rises from left to right
negative slope
falls from left to right
zero slope (slope of 0)
horizontal line
no slope/undefined
vertical line
slope of parallel lines
same slope
slope of perpendicular lines
opposite reciprocal (flip the fraction and change the sign)
collinear points
points that lie on the same line
midpoint formula
(x1 + x2/2, y1 + y2/2)
distance formula
d = √( x₂ - x₁)² + (y₂ - y₁)²
triangle inequality theorem
the sum of 2 sides must be greater than the third side, the difference of 2 sides must be less than the third side, the longest side of the triangle is opposite to the largest angle, the shortest side of the triangle is opposite to the smallest angle
isosceles triangle
2 congruent sides and 2 congruent angles, the altitude drawn from the vertex is also the median and angle bisector, if 2 sides of a triangle are congruent then the angles opposite
alternate interior angles
interior angles that lie on opposite sides of the transversal; congruent
corresponding angles
angles in the same place on different lines; congruent
alternate exterior angles
angles that lie outside a pair of lines and on opposite sides of a transversal; congruent
same-side interior angles
interior angles on the same side of the transversal; supplementary
congruent angles
having the same measure
supplementary angles
2 angles whose sum is 180 degrees
side-splitter theorem
if a line is parallel to a side of a triangle and intersects the other sides, then this line divides those 2 sides proportional