Math 329 Midterm 1

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Jorge732
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260086
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Math 329 Midterm 1
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2014-02-04 02:45:58
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Math 329
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Midterm 1
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  1. 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.
  2. Theorem 1
    • 1.Supplement of congruent angles
    • are congruent.

    • 2.Complement of congruent angles
    • are congruent.
  3. Theorem 2
    1. Vertical angles are congruent.
  4. 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
  5. 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.
  6. 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.
  7. Theorem 6 Every point on the perpendicular bisector of a segment
    is
    • 1.     
    • equidistant from the endpoints of
    • the segment.
  8. 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.
  9. 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.
  10. 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.
  11. Theorem 10:The Exterior
    Angle Theorem
    • 1.     
    • An exterior angle of a triangle
    • is greater than either of the remote interior angles.
  12. 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.
  13. Theorem 12 A point is on the angle bisector of an angle IFF
    • 1.     
    • it is equidistant from the sides
    • of the angle.
  14. Theorem 13    Given two non-congruent sides on a triangle,
    • 1.     
    • the angle opposite the longer
    • side is greater than the angle opposite the shorter side.
  15. Theorem 14 Given two non-congruent angles in a triangle,
    • 1.     
    • the side opposite the greater
    • angle is longer than the side opposite the smaller angle.
  16. 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.
  17. 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.
  18. Theorem 17 If two line in the same plane are each perpendicular
    to a third line in that plane
    1. then they are parallel.
  19. 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.
  20. Theorem 19 If two parallel lines are cut by a transversal,
    • 1. then a pair of corresponding
    • angles is congruent.
  21. Theorem 20 Two lines in a plane are parallel IFF
    • 1. a pair of corresponding angles
    • formed by a transversal is congruent.
  22. Theorem 21 Two lines in a plane are parallel IFF
    • 1. a pair of alternate interior
    • angles formed by a transversal are congruent.
  23. Theorem 22 Two lines are parallel IFF
    • 1. a pair of interior angles on the
    • same side of a transversal is supplementary.
  24. Theorem 23 The sum of the measures
    • 1. The sum of the measures of the
    • interior angles of a triangle is 180*.
  25. 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.
  26. Definition 3.10: Adjacent Angles
    • 1.     
    • Lie
    • in the same plane and share a common side and their interiors have no points in
    • common.
  27. Definition 3.11:
    Angle bisector
    • 1.     
    • Is
    • the common side of two adjacent angles of equal measure.
  28. Definition 3.12:
    Linear pair
    • 1.     
    • Is
    • 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*.
  29. Definition 3.13:
    Vertical angles
    • 1.     
    • are
    • angles which sides form two pairs of opposite rays.
  30. 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*
  31. 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
  32. 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.
  33. 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.
  34. 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
  35. Definition 6.1
    A kite is
    1. a quadrilateral that has two pairs of congruent adjacent sides.
  36. Definition 6.2
    A kite with all sides congruent is
    called a rhombus

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