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Postulate 5
 1.
 That, if a straight line falling
 on two straight lines makes the interior angles on the same side less than two
 right angles, the two straight lines, if produced indefinitely, meet on that
 side on which are angles less than the two right angles.

Theorem 1
 1.Supplement of congruent angles
 are congruent.
 2.Complement of congruent angles
 are congruent.

Theorem 2
1. Vertical angles are congruent.

Theorem 3: The
Isosceles Triangle Theorem
 1. If two sides of a triangle are
 congruent, then the angles opposite these sides are congruent
or
 2.The base angles of an isosceles
 triangle are congruent

Theorem 4: The Angle,
Side, Angle condition
 1. Given a one to one correspondence
 between the vertices of two triangles, if two angles and the included side of
 on triangle are congruent to the corresponding parts of the second triangle,
 the two triangles are congruent.

Theorem 5 The median of the base of an isosceles triangle
is
 1.
 perpendicular bisector as well as
 the angle bisector of the angle of the triangle.

Theorem 6 Every point on the perpendicular bisector of a segment
is
 1.
 equidistant from the endpoints of
 the segment.

Theorem 7The diagonal of a kite connecting the vertices
where the congruent sides intersect bisects the angles at these vertices and is
 1.
 the perpendicular bisector of the
 other diagonal.

Theorem 8: Side, Side,
Side Congruency condition
 1.
 Given a one to one correspondence
 among the vertices of two triangles, if the three sides of one triangle are
 congruent to the corresponding sides of the second triangle, then the triangles
 are congruent.

Theorem 9: Hypotenuse Leg
Congruence Condition
 1.
 If the hypotenuse and a leg of
 one triangle are congruent to the hypotenuse and a leg of another right
 triangle, then the triangles are congruent.

Theorem 10:The Exterior
Angle Theorem
 1.
 An exterior angle of a triangle
 is greater than either of the remote interior angles.

Theorem 11: Hypotenuse,
Acute Angle Congruence Condition
 1.
 If the hypotenuse and an acute
 angle of one right triangle are congruent to the hypotenuse and an acute angle
 of another right triangle, then the triangles are congruent.

Theorem 12 A point is on the angle bisector of an angle IFF
 1.
 it is equidistant from the sides
 of the angle.

Theorem 13 Given two noncongruent sides on a triangle,
 1.
 the angle opposite the longer
 side is greater than the angle opposite the shorter side.

Theorem 14 Given two noncongruent angles in a triangle,
 1.
 the side opposite the greater
 angle is longer than the side opposite the smaller angle.

Theorem 15: The Triangle
Inequality
1.The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Theorem 16: SAS
Inequality Theorem
 1.
 If in ∆ABC and ∆ XYZ we have AB = XY, AC = XZ, m.ang. A > m.ang. X, then BC > YZ, and conversely if BC > YZ, then m.ang. A > m.ang. X.

Theorem 17 If two line in the same plane are each perpendicular
to a third line in that plane
1. then they are parallel.

Theorem 18 If two lines are cut by a transversal and a pair of corresponding angles is congruent (or a pair of alternate interior angles is congruent),
1. then the lines are parallel.

Theorem 19 If two parallel lines are cut by a transversal,
 1. then a pair of corresponding
 angles is congruent.

Theorem 20 Two lines in a plane are parallel IFF
 1. a pair of corresponding angles
 formed by a transversal is congruent.

Theorem 21 Two lines in a plane are parallel IFF
 1. a pair of alternate interior
 angles formed by a transversal are congruent.

Theorem 22 Two lines are parallel IFF
 1. a pair of interior angles on the
 same side of a transversal is supplementary.

Theorem 23 The sum of the measures
 1. The sum of the measures of the
 interior angles of a triangle is 180*.

Definition 3.9 For any three points A,B, and C,
 1. we say that B is between A and C, and we write ABC, IFF A, B, and C are
 distinct, collinear points, and AB+ BC = AC.

Definition 3.10: Adjacent Angles
 1.
 Lie
 in the same plane and share a common side and their interiors have no points in
 common.

Definition 3.11:
Angle bisector
 1.
 Is
 the common side of two adjacent angles of equal measure.

Definition 3.12:
Linear pair
 1.
 Is
 formed by two adjacent angles in which the noncommon sides are opposite rays.
 The sum of the measures of two angles in a linear pair is 180*.

Definition 3.13:
Vertical angles
 1.
 are
 angles which sides form two pairs of opposite rays.

Definition 3.14
Supplementary/Complementary
 1.
 Supplementary
 angles: are angles which measure add up to 180*
 2.
 Complementary
 angles: are angles which measure add up to 90*

Definition 3.15
1. When 2 lines intersect they form four angles.
2. When a line intersects a segment at its midpoint and is perpendicular to thesegment
 1. if one of the angles is a right angle,
 then all the others are right angles, Then the lines are said to be
 perpendicular. We write m ┴ n.
 2., it is called the perpendicular bisector of the segment. M is the
 midpoint of AB. Then AM = MB or line AM cong. line MB

Definition 4.1:
Congruence of Triangles
 1.
 Triangles
 are congruent if there is a one to one correspondence between their vertices so
 that the corresponding sides are congruent and corresponding angles are
 congruent.

Definition 4.4
Acute and Obtuse triangles
1. A triangle is acute if all of its angles are acute.
2.A triangle is obtuse if one of its angles is obtuse.

Definition 5.1
Line segment connecting the vertex of a triangle with the midpoint of the opposite side is?
The segment from a vertex of a triangle
perpendicular to the line containing the opposite side is?
 1.
 The
 segment connecting the vertex of a triangle with the midpoint of the opposite
 side is called a median.
 The segment from a
 vertex of a triangle perpendicular to the line containing the opposite side is
 an altitude of the triangle

Definition 6.1
A kite is
1. a quadrilateral that has two pairs of congruent adjacent sides.

Definition 6.2
A kite with all sides congruent is
called a rhombus

