# Math 329 Midterm 1

 The flashcards below were created by user Jorge732 on FreezingBlue Flashcards. Postulate 5 1.     That, if a straight line fallingon two straight lines makes the interior angles on the same side less than tworight angles, the two straight lines, if produced indefinitely, meet on thatside on which are angles less than the two right angles. Theorem 1 1.Supplement of congruent anglesare congruent. 2.Complement of congruent anglesare congruent. Theorem 2 1. Vertical angles are congruent. Theorem 3: The Isosceles Triangle Theorem 1. If two sides of a triangle arecongruent, then the angles opposite these sides are congruent or 2.The base angles of an isoscelestriangle are congruent Theorem 4: The Angle, Side, Angle condition 1. Given a one to one correspondencebetween the vertices of two triangles, if two angles and the included side ofon 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 asthe 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 ofthe 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 theother diagonal. Theorem 8: Side, Side, Side Congruency condition 1.     Given a one to one correspondenceamong the vertices of two triangles, if the three sides of one triangle arecongruent to the corresponding sides of the second triangle, then the trianglesare congruent. Theorem 9: Hypotenuse Leg Congruence Condition 1.     If the hypotenuse and a leg ofone triangle are congruent to the hypotenuse and a leg of another righttriangle, then the triangles are congruent. Theorem 10:The Exterior Angle Theorem 1.     An exterior angle of a triangleis greater than either of the remote interior angles. Theorem 11: Hypotenuse, Acute Angle Congruence Condition 1.     If the hypotenuse and an acuteangle of one right triangle are congruent to the hypotenuse and an acute angleof 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 sidesof the angle. Theorem 13    Given two non-congruent sides on a triangle, 1.     the angle opposite the longerside is greater than the angle opposite the shorter side. Theorem 14 Given two non-congruent angles in a triangle, 1.     the side opposite the greaterangle 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 correspondingangles is congruent. Theorem 20 Two lines in a plane are parallel IFF 1. a pair of corresponding anglesformed by a transversal is congruent. Theorem 21 Two lines in a plane are parallel IFF 1. a pair of alternate interiorangles formed by a transversal are congruent. Theorem 22 Two lines are parallel IFF 1. a pair of interior angles on thesame side of a transversal is supplementary. Theorem 23 The sum of the measures 1. The sum of the measures of theinterior 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 aredistinct, collinear points, and AB+ BC = AC. Definition 3.10: Adjacent Angles 1.     Liein the same plane and share a common side and their interiors have no points incommon. Definition 3.11: Angle bisector 1.     Isthe common side of two adjacent angles of equal measure. Definition 3.12: Linear pair 1.     Isformed 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*. Definition 3.13: Vertical angles 1.     areangles which sides form two pairs of opposite rays. Definition 3.14 Supplementary/Complementary 1.     Supplementaryangles: are angles which measure add up to 180* 2.     Complementaryangles: 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 beperpendicular. We write m ┴ n. 2., it is called the perpendicular bisector of the segment. M is themidpoint of AB. Then AM = MB or line AM cong. line MB Definition 4.1: Congruence of Triangles 1.     Trianglesare congruent if there is a one to one correspondence between their vertices sothat the corresponding sides are congruent and corresponding angles arecongruent. 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.     Thesegment connecting the vertex of a triangle with the midpoint of the oppositeside is called a median. The segment from avertex of a triangle perpendicular to the line containing the opposite side isan 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 AuthorJorge732 ID260086 Card SetMath 329 Midterm 1 DescriptionMidterm 1 Updated2014-02-04T07:45:58Z Show Answers