properties
10 sides
decagon
rhombus
a=sh (a=1/2 d1d2)
p=4s
trapezoid
1 pair of opposite sides is parallel (quadrilateral with at least 1 pair of parallel sides)
isosceles trapezoid: 1 pair of opposite sides is parallel, diagonals are equal, non parallel sides are equal, 2 base angles are equal
inscribed angles of a circle (theorem)
inscribed angles with the same arcs are equal.
an inscribed angle is formed from 2 chords of a circle meeting at a point on the circle. the inscribed angles containing the same arc are equal.
arc length formula
θ/360 * 2πr
7 sides
heptagon (septagon)
trapezoid
a=1/2(b1+b2)h
p=a1+b1+a2+b2
kite
2 pairs of adjacent sides are equal, 1 pair of opposite sides are equal, diagonals bisect each other at 90°
what are the types of quadrilaterals
square, rectangle, parallelogram, rhombus, trapezoid, kite
area of a sector formula
θ/360 * πr2
dedecagon
12 sides
kite
a=1/2 d1d2
p=2(a+b)
rhombus
opposite sides are parallel, diagonals bisect a pair of opposite angles. all sides are equal, opposite angles are equal, diagonals bisect each other at 90°
parallelogram with all 4 congruent sides & opposite angles are equal
tangent line to a circle (theorem)
a tangent line is a line that is drawn from outside of the circle and touches at exactly 1 point (point of tangency)
a tangent line is perpendicular to the radius/diameter drawn to the point of tangency
the central angle is
hendecagon
11 sides
square
a=1/2 d2
parallelogram
opposite sides are equal and parallel, opposite angles are equal, 2 consecutive angles are supplementary, diagonals bisect each other
quadrilateral with 2 pairs of opposite & parallel sides & angles are congruent.
total interior angle
(n-2)*180
inscribed triangles in a semicircle
a triangle inscribed in a semicircle is a right triangle. The hypotenuse is the diameter (the inscribed angle is half (90°) of the central angle (180°))
9 sides
nonagon
parallelogram
a=bh
p=2(b+a)
total number of points on a circle formula
circumference of a circle/distance between each point
total exterior angle
(n-2)*180/n
each exterior angle must be 360/n
radius/diameter theorem
a radius/diameter perpendicular to a chord bisects the chord and its arc