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60 Cards in this Set

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Theorem 1-1
if two lines intersect, then they intersect in exactly one point
Theorem 1-2
Through a line and a point not in the line there is exactly one plane
Theorem 1-3
If two lines intersect, then exactly one plane contains the lines
Theorem 2-1 (Midpoint Theorem)
If M is the midpoint of (segment) AB, then AM=1/2AB and MB=1/2AB
Theorem 2-2 (Angle Bisector Theorem)
if (ray) BX is the bisector of angle ABC, then m(angle)ABX=1/2 m(angle)ABC and m(angle)XBC=1/2 m(angle)ABC
Theorem 2-3
Vertical angles are congruent
Theorem 2-4
If two lines are perpendicular, then they form congruent adjacent angles
Theorem 2-5
If two lines form congruent adjacent angles, then the lines are perpendicular
Theorem 2-6
If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary
Theorem 2-7
If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent
Theorem 2-8
If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent
Theorem 3-1
If two parallel planes are cut by a third plane, then the lines of intersection are parallel
Theorem 3-2
If two parallel lines are cut by a transversal, then alternate interior angles are congruent
Theorem 3-3
If two parallel lines are cut by a tranversal, then same-side interior angles are supplementary
Theorem 3-4
if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also
Theorem 3-5
If two lines are cut by the transversal and alternate interior angles are congruent, then the lines are parallel
Theorem 3-6
If two lines are cut by a transversal and same-side interior angles are supplementary , then and lines are parallel
Theorem 3-7
In a plane two lines perpendicular to the same line are parallel
Theorem 3-8
Through a point outside a line, there is exactly one line parallel to the given line
Theorem 3-9
Through a point outside a line, there is exactly one line perpendicular to the given line
Theorem 3-10
two lines parallel to a third line are parallel to each other
Theorem 3-11
The sum of the measures of the angles of a triangle is 180
Theorem 3-11 Corollary 1
if two angles of one triangle are congruent to two angles of another triangle, the the third angles are congruent
Theorem 3-11 Corollary 2
Each angle of an equiangular triangle has measure 60
Theorem 3-11 Corollary 3
In a triangle, there can be at most one right angle or obtuse angle
Theorem 3-11 Corollary 4
The acute angles of a right triangle are complementary
Theorem 3-12
The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles
Theorem 3-13
The sum of the measures of the angles of a convex polygon with n sides is (n-2)180
Theorem 3-14
The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex is 360
Theorem 4-1 (Isosceles Triangle Theorem)
If two sides of a triangle are congruent, then the angles opposite those sides are congruent
Theorem 4-1 Corollary 1
An equilateral triangle is also equiangular
Theorem 4-1 Corollary 2
An equilateral triangle has three 60 degree angles
Theorem 4-1 Corollary 3
The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint
Theorem 4-2
If two angles of a triangle are congruent, then the sides opposite those angles are congruent
Theorem 4-2 Corollary 1
An equiangular triangle is also equilateral
Theorem 4-3 (AAS Theorem)
If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent
Theorem 4-4 (HL Theorem)
If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent
Theorem 4-5
If a point lies on the perpendicular bisector of a segment, then the point is equidistant for the endpoints of the segment
Theorem 4-6
If a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment
Theorem 4-7
If a point lies on the bisector of an angle, then the point is equidistant from the sides of the angle
Theorem 4-8
If a point is equidistant from the sides of an angle. then the point lies on the bisector of the angle
Theorem 5-1
Opposite sides of a parallelogram are congruent
Theorem 5-2
Opposite angles of a parallelogram are congruent
Theorem 5-3
Diagonals of a parallelogram bisect each other
Theorem 5-4
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram
Theorem 5-5
If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram
Theorem 5-6
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallogram
Theorem 5-7
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram
Theorem 5-8
if two lines are parallel, then all points on one line are equidistant from the other line
Theorem 5-9
If three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal
Theorem 5-10
a line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side
Theorem 5-11
The segment that joins the midpoints of two sides of a triangle
(1) is parallel to the third side
(2) is half as long as the third side
Theorem 5-12
Diagonals of a rectangle are congruent
Theorem 5-13
The diagonals of a rhombus are perpendicular
Theorem 5-14
Each diagonal of a rhombus bisects two angles of the rhombus
Theorem 5-15
The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices
Theorem 5-16
If an angle of a parallelogram is a right angle, then the parallelogram is a rectangle
Theorem 5-17
If two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus
Theorem 5-18
Base angles of an isosceles trapezoid are congruent
Theorem 5-19
The median of a trapezoid
(1) is parallel to the bases
(2) has a length equal to the average of the base lengths.