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70 Cards in this Set

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Theorem 1
Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other (SAS)
Corollary 1-1
Two right triangles are congruent if the two legs of the other (L.L.)
Corresponding parts of congruent triangles are equal
C.P.C.T.E.
Theorem 2
Two triangles are congruent if a side and the two adjacent angles of one are equal respectively to a side and the two adjacent angles of the other (A.S.A.)
Corollary 2-1
Two right triangles are congruent if a leg and the adjacent acute angle of one are equal respectively to a leg and the adjacent acute angle of the other (L.A)
Theorem 3
In any isosceles triangle the angles opposite the equal sides are equal.
Corollary 3-1
An equilateral triangle is also equiangular
Theorem 4
Two triangles are congruent if the three sides of one are equal respectively to the three sides of the other (SSS)
Theorem 5
An exterior angle of a triangle is greater then either opposite interior angle.
Coorollary 5-1
One and only one perpendicular can be drawn to a line from a point outside the line
Theorem 6
If two angles of a triangle are equal, the sides opposite those angles are equal
Corollary 6-1
An equiangular triangle is also equilateral
Theorem 7
When two straight lines are cut by a transversal if a pair of alternate interior angles are equal the two straight lines are parallel
Corollary 7-1
When two straight lines are cut by a transversal if two corresponding angles are equal the two straight lines are parallel
Corollary 7-2
Two lines perpendicular to the same straight \line are parallel
corollary 7-3
When two straight lines are cut by a transversal if the sum of the two interior angles on the same side of the transversal is equal to a straight angle the two straight lines are parallel
Theorem 8
If two parallel lines are cut by a transversal the alternate interior angles are equal
Corollary 8-1
If two parallel lines are cut by a transversal then the corresponding angles are equal
Corollary 8-2
If two parallel lines are cut by a transversal then the sum of the two interior angles on the same side of the transversal is equal to a straight angle.
Corollary 8-3
When two straight lines are cut by a transversal if the sum of the interior angles on the same side of the transversal does not equal a straight angle then the two lines are not parallel
Corollary 8-4
A straight line perpendicular to one of two parallel lines is perpendicular to the other also
Corollary 8-5
Lines perpendicular to nonparallel lines are not parallel
Theorem 9
If two angles have their sides parallel right side to right side and lift lide to left side the angles are equal
Corollary 9-1
If two angles have their sides parallel right side to left side and left side to right side the angles are supplementary
Theorem 10
If two angles have their sides perpendicular right side to right side and left side to left side the angles are equal
Corollary 10-1
If two anles have their sides perpendicular right side to left side and left side to right side the angles are supplementary
Theorem 11
The sum of the angles of a triangle is a straight angle
Corollary 11-1
An exterior angle of a triangle is equal to the sum of the two opposite interior angles
corollary 11-2
In any triangle there can be but one right angle or obtuse angle.
Corollary 11-3
In any right triangle the two acute angles are complementary
Corollary 11-4
If an acute angle of one right triangle equals an acute angle of another right triangle the remaining acute angles of the two triangles are equal
Corollary 11-5
Two right triangles are congruent if the hypotenuse and an acute angle of one are equal respectively to the hypotenuse and an acute angle of the other (H.A.)
Corollary 11-6
Two right triangles are congruent if a leg and either acute angle of one are equal respectively to a leg and the corresponding acute angle of the other (L.A.)
Corollary 11-7
If two angles of one triangle are equal respectively to two angles of another then the third angle of the first is equal to the third angle of the second
Corollary 11-8
Two triangles are congruent if a side and any two angles of one are equal respecively to a corresponding side and two angles of the other (S.A.A.)
Corrollary 11-9
Each angle of an equilateral triangle is 60 degrees
Theorem 12
Two right triangles are congruent if the hypotenuse and a leg of one are equal respectively to the hypotenuse and a leg of the other (H.L.)
Corollary 12-1
The perpendicular from the vertex to the base off an isosceles triangle visects the base and also the vertex angle
Theorem 13
If one side of a triangle is greater than a second side the opposite the first side is greater than the angle opposite the second side
Theorem 14
If one angle of a triangle is greater than a second angle the side opposite the first angle is greater than the side opposite the second angle.
Corollary 14-1
The perpendicular is the shortest line that can ve drawn from a given point to a given line
Corollary 14-2
If a line is the shortest line that can be drawn from a given point to a given line then it is a perpendicular from the point to the given line
Theorem 15
If two straight lines drawn from a point in a perpendicular to a given line cut off equal segments from the foot of the perpendicular then they are equal
Corollary 15-1
If two straight lines drawn from a point in a perpendicular to a given line cut off unequal segments from the foot of the perpendicular then the straight line that cuts off the greater segment is the greater straight line
Theorem 16
If two straight lines drawn from a point in a perpendicular to a given line are equal then they cut off equal segments from the foot of the perpendicular
Corollary 16-1
If two straight lines drawn from a point in a perpendicular to a given line are unequal then the freater cuts off the greater sefments from the foot of the perpendicular
Theorem 17
If two triangles have two sides of one equal respectively to two sides of the other and the included angles are unequal then the triangle which has the greater included angle has the greater third side
Theorem 18
If two triangles have two sides of one equal respectively to two sides of the other and the third sides are unequal then the triangle which has the greater third side has the greater angle opposite the third side
Theorem 19
The opposite sides of a parallelogram are equal and the opposite angles are equal
Corollary 19-1
All the sides of a rhombus are equal and all the sides of a square are equal
Corollary 19-2
A diagonal divides a parallelogram into two congruent triangles
Corollary 19-3
Parallel lines included between parallel lines are equal
Corollary 19-4
`Two parallel lines are everywhere the same distance apart
Theorem 20
The diaonals of a parallelogram bisect each other
Theorem 21
If the opposite sides of a quuadrilateral are equal then the figure is a parallelogram
Theorem 22
If two sides of a quadrilateral are equal and parallel then the figure is a parallelogram
Theorem 23
If the diagonals of a quadrilateral bisect each other then the figure is a parallelogram
Theorem 24
If three or more parallels cut off equal segments on one transversal they cut off equal segments on any other transversal
Corollary 24-1
The line parallel to one side of a triangle and bisecting a second side biseccts the third side
Theorem 25
The line that joins the midpoints of two sides of a triangle is parallel to the third side and equals half the third side
Theorem 26
The sum of the angles of a polygon of n sides is (n-2) straight angles
Corollary 26-1
In an equiangular polygon of n sides each angle equals [(n-2) divided by n] straight angles
Corollary 26-2
The sum of the exteriior angles of a polygon made by extending each of its sides in succession is equal to two straight angles
Theorem 27
(a) Ebery point in the perpendicular bisector of a line is equidistant from the ends of that line
(b) Every point equidistant from the ends of a line lies in the perpendicular bisector of that line
Corollary 27-1
Two points each equidistant from the ends of a line determine the perpendicular bisector of that line
Theorem 28
(a) Every point in the bisector of an angle is equidistant from the sides of that angle
(b) Every point eequidistant from the sides of an angle lies in the bisector of that angle
Theorem 29
The perpendicular bisectors of the sides of a triangle meet in a point which is equidistant from the three vertices
Corollary 29-1
The three altitudes of a triangle meet in a point
Theorem 30
The visectors of the angles of a triangle meet in a point which is equidistant from the three sides
Theorem 31
The medians of a triangle meet in a point which is two thirds of distance from each vertex to the midpoint of the opposite side