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
it is equidistant from the sides
of the angle.
Theorem 13 Given two non-congruent sides on a triangle,
the angle opposite the longer
side is greater than the angle opposite the shorter side.
Theorem 14 Given two non-congruent angles in a triangle,
the side opposite the greater
angle is longer than the side opposite the smaller angle.
Theorem 15: The Triangle
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
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 A-B-C, IFF A, B, and C are
distinct, collinear points, and AB+ BC = AC.
Definition 3.10: Adjacent Angles
in the same plane and share a common side and their interiors have no points in
the common side of two adjacent angles of equal measure.
formed by two adjacent angles in which the non-common sides are opposite rays.
The sum of the measures of two angles in a linear pair is 180*.
angles which sides form two pairs of opposite rays.
angles: are angles which measure add up to 180*
angles: are angles which measure add up to 90*
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
Congruence of 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
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.
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?
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
A kite is
1. a quadrilateral that has two pairs of congruent adjacent sides.