1.
30 60 90 triangle theorem: in a 30 60 90 triangle, the length of the hypotenuse is twice the length of the shorter leg. the length of the longer leg is square root of 3 times the length of the shorter leg.
hypotenuse=2 times shorter leg
longer leg= square root of three times shorter leg
2.
45 45 90 triangle theorem: in a 45 45 90 triangle both legs are congruent and the length of the hypotenuse is square root of 2 times the length of a leg
hypotenuse=square root of 2 times leg
3.
angle bisector theorem: if a point is on the bisector of an angle, then the point is equidistant from the sides of the angle.
4.
arc addition postulate: the measure of the arc formed by two adjacent arcs is the sum of the measure of the two arcs.
5.
arc length: the length of an arc of a circle is the product of the ratio measure of the arc divided by 360 and the circumference of the circle
length of arc ab=measure of arc ab over 360 times 2pieR
6.
arc of a circle: a=pie R squared
7.
area of a rectangle: the area of a rectangle is the product of its base and height. a=bh
8.
area of a regular polygon: a=1/2ap
9.
area of a rhombus or kite: a=1/2d(1)d(2)
10.
area of a sector of a circle: the area of a sector of a s=circle is the product of the ratio measure of the arc over 360 and the circle.
11.
area of a triangle: the area of a triangle is half the product of base and the corresponding height a=1/2bh
12.
area of parallelogram: the area of a parallelogram is the product of a base and the corresponding height. a=bh
13.
area of trapezoid: a=1/2h(b1+b2)
14.
circumference of a circle: c=pie times diameter or C=pie times radius squared
15.
converse of the angle bisector theorem: if a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector.
16.
corollary to the triangle exterior angle theorem: the measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles
17.
perpendicular bisector theorem: if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment
18.
Pythagorean theorem: in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. a(squared) +b(squared)=c(squared)
19.
theorem 5-6: the perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices
20.
theorem 5-7: the bisectors of the angles of a triangle are concurrent at a point equidistant from the sides
21.
theorem 5-8: the medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite side
22.
theorem 5-9: the lines that contain the altitudes of a triangle are concurrent
23.
theorem 5-10: if the two sides of a triangle are not congruent then the larger angle lies opposite the longer side.
24.
theorem 5-11: if two angles of a triangle are not congruent, then the longer side lies opposite the larger angle.
25.
theorem 6-1: opposite sides of a parallelogram are congruent
26.
theorem 6-2: opposite angles of a parallelogram are congruent
27.
theorem 6-3: the diagonals of a parallelogram bisect each other
28.
theorem 6-4: if three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal
29.
theorem 6-5: if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram
30.
theorem 6-6: if one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram
31.
theorem 6-7: if both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram
32.
theorem 6-8: if both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram
33.
theorem 6-9: each diagonal of a rhombus bisects two angles of the rhombus
34.
theorem 6-10: the diagonals of a rhombus are perpendicular.
35.
theorem 6-11: the diagonals of a rectangle are congruent
36.
theorem 6-12: if one diagonal of a parallelogram bisects two angles of the parallelogram, then the parallelogram is a rhombus
37.
theorem 6-13: if the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus
38.
theorem 6-14: if the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle
39.
theorem 6-15: the base angles of an isosceles trapezoid are congruent
40.
theorem 6-16: the diagonals of an isosceles trapezoid are congruent
41.
theorem 6-17: the diagonals of a kite are perpendicular
42.
theorem 7-6: if the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, the triangle is obtuse. is c2>a2+b2 the triangle is obtuse
43.
theorem 7-6: if the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, the triangle is obtuse.
44.
theorem 7-7: if c2<a2+b2 then it is acute
45.
trapezoid midsegment theorem: 1) the midsegment of a trapezoid is parallel to the bases.
20 the length of the midsegment of a trapezoid is half the sum of the lengths of the bases
46.
triangle inequality theorem: the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
47.
triangle midsegment theorem: if a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side, and is half its length
