1) Two points determine a line. |
2) Three noncollinear points determine a plane. |
3) If 2 lines intersect, then their intersection is a
point. |
4) If 2 planes intersect, then their intersection is a
line. |
5) Through a line and a point not on that line, there is
exactly 1 plane. |
6) Ruler Postulate - |
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7) Segment Addition Postulate - |
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8) Protractor Postulate - |
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9) Angle Addition Postulate - |
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10) Vertical Angle Theorem - Vertical angles are
congruent. |
11) Congruent Supplements Theorem - If two angles are
supplements of congruent angles ( or the same angle), then the two angles
are congruent. |
12) Congruent Complements Theorem - If two angles are
complements of congruent angles ( or the same angle), then the two angles
are congruent. |
13) Triangle - Angle - Sum Theorem - The sum of the
interior angles of a triangle is 180. |
14) Exterior Angle Theorem - The exterior angle of a
triangle is equal to the sum of its remote interior angles. |
15) Arc Addition Postulate - |
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16) Two sides of a triangle are congruent if and only if the
angles opposite them are congruent. |
17) The bisector of the vertex angle of an isosceles
triangle is the perpendicular bisector of its base. |
18) A triangle is equilateral if and only if it is
equiangular. |
19) If a triangle is a right triangle, then the acute angles
are complementary. |
20) If two angles of one triangle are congruent to two
angles of another triangle, then the third angles are congruent. |
21) All right angles are congruent. |
22) If two angles are supplementary and congruent, then each
angle is a right angle. |
23) Triangle Midsegment Theorem - If a segment joins
the midpoints of two sides of a triangle, then the segment formed is
parallel to the third side and one-half its length. |
24) Perpendicular Bisector Theorem and Converse - A
point is on the perpendicular bisector of a segment if and only if it is
equidistant from the endpoints of the segment. |
25) Angle Bisector Theorem and Converse - A point is
on the bisector of an angle if and only if it is equidistant from the
sides of the angle. |
26) Corresponding Angle Postulate - If two parallel
lines are cut by a transversal, then corresponding angles are
congruent. |
27) Alternate Interior Angle Theorem - If two
parallel lines are cut by a transversal, then alternate interior angles
are congruent. |
28) Same - Side Interior Angle Theorem - If two
parallel lines are cut by a transversal, interior angles on the same side
of the transversal are supplementary. |
29) Converse of the Corresponding Angle Postulate -
If two lines are cut by a transversal so that corresponding angles are
congruent, then the lines are parallel. |
30) Converse of the Alternate Interior Angle Theorem
- If two lines are cut by a transversal so that alternate interior angles
are congruent, then the lines are parallel. |
31) Converse of the Same - Side Interior Angle
Theorem - If two lines are cut by a transversal so that same side
interior angles are supplementary, then the lines are parallel. |
32) SSS - If three sides of one triangle are
congruent to three sides of another triangle, then the triangles are
congruent. |
33) SAS - If two sides and an included angle of one
triangle are congruent to two sides and an included angle of another
triangle, then the triangles are congruent. |
34) ASA - If two angles and an included side of one
triangle are congruent to two angles and an included side of another
triangle, then the triangles are congruent. |
35) AAS - If two angles and a nonincluded side of one
triangle are congruent to two angles and the corresponding nonincluded
side of another triangle, then the triangles are congruent. |
36) HL - If the hypotenuse and a leg of one right
triangle are congruent to a corresponding hypotenuse and leg of another
right triangle, then the triangles are congruent. |
37) Opposite sides of a parallelogram are congruent. |
38) Opposite angles of a parallelogram are congruent. |
39) Diagonals of a parallelogram bisect each other. |
40) If three or more parallel lines cut off congruent
segments on one transversal, then they cut off congruent segments on every
transversal. |
41) If the diagonals of a quadrilateral bisect each other,
then the quadrilateral is a parallelogram. |
42) If one pair of opposite sides of a quadrilateral are
both congruent and parallel, then the quadrilateral is a
parallelogram. |
43) If both pairs of opposite sides of a quadrilateral are
congruent, then the quadrilateral is a parallelogram. |
44) If both pairs of opposite angles of a quadrilateral are
congruent, then the quadrilateral is a parallelogram. |
45) Diagonals of a rhombus bisect the rhombus's
angles. |
46) Diagonals of a rhombus are perpendicular. |
47) Diagonals of a rectangle are congruent. |
48) Base angles of an isosceles trapezoid are
congruent. |
49) Diagonals of an isosceles trapezoid are congruent. |
50) Diagonals of a kite are
perpendicular. |