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2014-03-17 23:39:43

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


    2.The base angles of an isosceles triangle are congruent
  2. 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.
  3. Theorem 7 The diagonal of a kite connecting the vertices where the congruent sides intersect
    1.The diagonal of a kite connecting the vertices where the congruent sides intersect bisects the angles at these vertices and is the perpendicular bisector of the other diagonal.
  4. Theorem 10:The Exterior Angle Theorem
    1.An exterior angle of a triangle is greater than either of the remote interior angles.
  5. 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.
  6. Theorem 19 If two parallel lines are cut by a transversal, then
    1.If two parallel lines are cut by a transversal, then a pair of corresponding angles is congruent.
  7. Theorem 24 The measure of an exterior angle in a triangle is
    1.The measure of an exterior angle in a triangle is equal to the sum of the measure of its two remote angles.
  8. Theorem 31: The Midsegment Theorem
    1.The segment connecting the midpoints of two sides of a triangle is parallel to the third and half as long as that side.
  9. Theorem 33 Suppose the angle formed by
    a tangent and a chord is acute.
    1.Suppose the angle formed by a tangent and a chord is acute. Then the measure of this angle equals half the measure of the intercepted arc.
  10. Theorem 36 The area of a rectangle with sides of length a and b is
    1.The area of a rectangle with sides of length a and b is ab.
  11. Theorem 39 The area of a trapezoid whose bases have length a and b and whose height is h is
    1.The area of a trapezoid whose bases have length a and b and whose height is h is given by 1/2(a + b)h.
  12. Theorem 50 If f is a linear transformation and A, B and C are non-collinear points, then
    • If f is a linear transformation and A, B and C are
    • non-collinear points, then f(A) , f(B), and f(C) are also non-collinear
  13. Theorem 52 ABCD Property
    Reflections are:

    • A. Angle-measure preserving
    • B. Betweenness Preserving
    • C. Collinearity preserving
    • D. Distance preserving
  14. Theorem 54 The product of two lines reflections sl and sm where l and m are parallel lines, is
    The product of two lines reflections sl and sm where l and m are parallel lines, is distance and slope preserving, and maps a given line n to one that is parallel to it.