Download Postulate 3

my notes of mathyness
11/19/2013 6:33:00 PM
According to the games that I played, a rhombus is any shape with four
sides.
A square is a rhombus in which all sides are equal and all angles are right
angles
A kite is a little thing made of fabric that people like to fly in the park
A rectangle is a shape that is like a square except only pairs of sides are
congruent
An isosceles trapezoid is like an isosceles triangle with the top cut off
A kite is basically a diamond shape
Inscribed square: a circle with a square in it that touches the edge but does
not overlap it
(n=number of sides) n-2 x 180=total measure of interior angles
parallelogram: a quadrilateral with both pairs of opposite sides have equal
length
11/19/2013 6:33:00 PM
Theorem 4: Vertical angles are congruent
Theorem 4: (SSS) If three sides of one triangle are congruent to three
sides of the other triangle then the two triangles are congruent.
Theorem 5: (SAS) If two sides of a triangle and the included angle are
congruent to the two sides, and an included angle of another triangle are
congruent, then the triangles themselves are congruent.
Theorem 6: (ASA) If two angles of a triangle and the included side are
congruent to the two angles and an included side of another triangle, then
the triangles themselves are congruent.
Theorem 7: (AAS) Is another form of ASA
Theorem 8: (HL) If the hypotenuse and one leg of a right triangle is
congruent to the hypotenuse and leg of another, then the right triangles are
congruent.
Theorem 9: (Triangle-Sum Theorem) The measure of the interior angles of
a triangle = 180 degrees.
Theorem 10: (Third Angle Theorem) If two angles from one triangle are
congruent to the two angles of another triangle, then the two triangles are
congruent.
Theorem 11: (Kite Symmetry Theorem) The line containing the ends of a
kite is a symmetry line for the kite
Theorem 12: (Isosceles Triangle Theorem) The base angles of an isosceles
triangles are congruent
Theorem 3: Supplements of congruent angles are congruent
Theorem 2: On any line L, there are five different points on L.
Theorem 1: If P is the midpoint of TF, then PF= TF.
rectangles are parallelograms if and only if the diagonals are congruent
Proposition 1: If two angles form a linear pair and are congruent, then
they are right angles.
in a parallelogram the opposite sides are of equal length
in a parallelogram the opposite sides are congruent
if the diagonal bisect teach other then the quadrilateral is a parallelogram
if a quadrilateral is a parallelogram then its consecutive sides are
complementary
a quadrilateral is a parallelogram if and only if the diagonals bisect each
other
11/19/2013 6:33:00 PM
Postulate 1: Two points determine a line.
Postulate 2: Every line is a set of points that can be put into a one-to-one
correspondence with the real numbers, with any point on it corresponding to
0 and any other point corresponding to 1.
*Ruler Postulate-> the idea of matching up the points on a line with real
numbers.
Postulate 3:
There are at least two points in space.
Given a line in a plane, there is at least one point in the plane that is not on
the line.
Given a plane in space, there is at least one point in space that is not in the
plane.
Postulate 4: (Angle Measurement Postulate) You can match up every angle
with a number between 0 and 180.
Postulate 5: Linear pair -> supplementary.
Postulate 6: (Angle Addition Postulate) For any two angles, angle AOB and
angle BOC, if A-B-C, then the measure of angle AOB + the measure of BOC
= the measure of AOC.
Postulate 7: (SSS) If three sides of one triangle are congruent to three
sides of the other triangle then the two triangles are congruent.
Postulate 8: (SAS) If two sides of a triangle and the included angle are
congruent to the two sides, and an included angle of another triangle are
congruent, then the triangles themselves are congruent.
Postulate 9: (ASA) If two angles of a triangle and the included side are
congruent to the two angles and an included side of another triangle, then
the triangles themselves are congruent.
Postulate 10: (AAS) Is another form of ASA
Postulate 11: (HL) If the hypotenuse and one leg of a right triangle is
congruent to the hypotenuse and leg of another, then the right triangles are
congruent.
11/19/2013 6:33:00 PM
our group: Me, Nicholas, and Isaac
our proofs: in a parrallelagram the opposite sides are congruent
a quadrilateral is a parralelagram if and only if the diagnals bisect each other