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