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70 Cards in this Set
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 Back
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 11

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 21

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 31

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 51

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 61

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 71

When two straight lines are cut by a transversal if two corresponding angles are equal the two straight lines are parallel


Corollary 72

Two lines perpendicular to the same straight \line are parallel


corollary 73

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 81

If two parallel lines are cut by a transversal then the corresponding angles are equal


Corollary 82

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 83

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 84

A straight line perpendicular to one of two parallel lines is perpendicular to the other also


Corollary 85

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 91

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 101

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 111

An exterior angle of a triangle is equal to the sum of the two opposite interior angles


corollary 112

In any triangle there can be but one right angle or obtuse angle.


Corollary 113

In any right triangle the two acute angles are complementary


Corollary 114

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 115

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 116

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 117

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 118

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 119

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 121

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 141

The perpendicular is the shortest line that can ve drawn from a given point to a given line


Corollary 142

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 151

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 161

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 191

All the sides of a rhombus are equal and all the sides of a square are equal


Corollary 192

A diagonal divides a parallelogram into two congruent triangles


Corollary 193

Parallel lines included between parallel lines are equal


Corollary 194

`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 241

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 (n2) straight angles


Corollary 261

In an equiangular polygon of n sides each angle equals [(n2) divided by n] straight angles


Corollary 262

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 271

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 291

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
