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44 Cards in this Set

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post 1 (ruler post)
The points on a line can be paired with real numbers in such a way that any two points can have coordinates 0 and 1
post 2 (seg add post)
if B is between A and C, then AB+BC=AC
post 4 (angle add post)
m∠AOB+m∠BOC=m∠AOC
post 5
a line contains at least 2 pts, a plane contains at least 3 pts, space contains at lest 4 pts not all in one plane
post 6
through any 2 pts there is exactly 1 line
post 7
through any 3 pts there is at least 1 plane, through any 3 noncollinear pts there is exactly 1 plane
post 8
if 2 pts are in a plane then, the line that contains the pts is in that plane
post 9
if 2 planes intersect, their intersection is a line
post 10
if 2 parallel lines are cut by a transversal, then corresponding angles are congruent
post 11
if 2 lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel
post 12 (sss post)
3 sides of 2 triangles congruent, both triangles are congruent
post 13 (sas post)
if 2 sides and the included angle of 2 triangles are congruent, both triangles are congruent
post 14 (asa post)
if 2 angles and the included side of 2 triangles are congruent, both triangles are congruent
th 1-1
if 2 lines intersect, they intersect in exactly 1 pt
th 1-2
through a line and a pt not in the line there is exactly 1 plane
th 1-3
if 2 lines intersect, then exactly 1 plane contains the lines
th 2-1 (midpt th)
if M is the midpt of AB, then AM=1/2AB and MB=1/2AB
th 2-2 (angle bisector th)
if BX is the bisector of ∠ABC, then m∠ABX=1/2m∠ABC and m∠XBC=1/2m∠ABC
th 2-3 (vert angle th)
vertical angles are congruent
th 2-4
if 2 lines are perp, then they form congruent adjacent angles
th 2-5
if 2 lines form congruent adjacent angles, then the lines are perp
th 2-6
if the exterior sides of 2 adjacent acute angles are perp, then the angles are complementary
th 2-7
if 2 angles are supplements of congruent angles (or of the same angle), the 2 angles are congruent
th 2-8
if two angles are complements of congruent angles (or of the same angle), the 2 angles are congruent
th 3-1
if 2 parallel planes are cut by a 3rd plane, the lines of intersection are parallel
th 3-2
if 2 parallel lines are cut by a transversal, the alternate interior angles are congruent
th 3-3
if 2 parallel lines are cut by a transversal, the same-side int angles are supplementary
th 3-4
if a trasversal is perp to 1 of 2 parallel lines, then it is perp to the other also
th 3-5
if 2 lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel
th 3-6
if 2 lines are cut by a transversal and same-side interior angles are supplementary, the lines are parallel
th 3-7
in a plane 2 lines perp to the same line are parallel
th 3-8
through a pt outside a line, there is exactly one line parallel to the given line
th 3-9
through a pt outside a line, there is exactly 1 pt perp to the given line
th 3-10
2 lines parallel to a 3rd line are parallel to each other
th 3-11
the sum of the measures of the angles of a triangle is 180
corr1 if 2 angles of 2 triangles are congruent to each other, then the third angles are congruent
corr2 angles of an equilateral triangle are each 60
corr3 in a triangle, there can be at most 1 rt angle or 1 obtuse angle
corr4 the acute angles of a rt triangle are complementary
th 3-12
the measure of an exterior angle of a triagle equals the sum of the 2 remote interior angles
th 3-13
the sum of the measures of the angles of a convex polygon with n sides is (n-2)180
th 3-14
the sum of the exterior angles of any convex polygon is 360
th 4-1 (isoc triangle th)
if two sides of a triangle are congruent, then angles opposite those sides are congruent
corr1 an equilateral triangle is also equiangular
corr2 equilateral triangle has 3 60 degree angles
corr3 the bisector of the vertex angle of an isoc triangle is perp to the base at its midpt
th 4-2
if 2 angles of a triangle are congruent, the sides opposite those angles are congruent
corr1 an equiangular triangle is equilateral
th 4-3 (AAS post)
if 2 angles and a non-included side of 1 triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent
th 4-4 (HL th)
if the hypotenuse and a leg of a rt triangle are congruent to corresponding parts of another triangle, the 2 triangles are congruent
th 4-5
if a pt lies on the perp bisector of a segment, then the pt is equidistant from the endpts of the segment
th 4-6
if a pt is equidistant from the endpts of a segmt, the pt lies on the perp bisector of the segmt