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17. It is possible to locate three points in such a position that an unlimited number of' planes contain all three points. True
18. It is possible for two intersecting lines to be noncoplanar. False
19. Through any three points there is at least one line. False
20. If points A and B lie in plane P, then so does any point of Ray AB. True

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12. If today is Friday, then tomorrow is Saturday. True
13. If x > 0, then x2 > 0. False
14. If a number is divisible by 6, then it is divisible by 3. True
15. If 6x=18 then x=3
3. True

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15. Two skew lines are never parallel.
16. Two parallel lines are always coplanar.
17. A line in the plane of the ceiling and a line in the plane of' the floor are sometimes parallel.
18. Two lines in the plane of' the floor are never skew.
19. A line in the plane of' a wall and a line in the plane of' the floor are
a. sometimes parallel. b. sometimes intersecting. c. sometimes skew.

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30. When there is a transversal of two lines, the three lines are always coplanar.
31. Three lines intersecting in one point are sometimes coplanar.
32. Two lines that are not coplanar never intersect.
33. Two lines parallel to a third line are always parallel to each other.
34. Two lines skew to a third line are sometimes skew to each other.
35. Two lines perpendicular to a third line are sometimes perpendicular to each other.
36. Two planes parallel to the same line are sometimes parallel to each other.
37. Two planes parallel to the same plane are always parallel to each other.
38. Lines in two parallel planes are sometimes parallel to each other.
39. Two lines parallel to the same plane are sometimes parallel to each other.

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1. If' a triangle is isosceles, then it is sometimes equilateral.
2. If a triangle is equilateral, then it is always isosceles
3. If a triangle is scalene, then it is never isosceles.
4. If a triangle is obtuse, then it is sometimes isosceles.

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1. If' Line AB intersects Segment CD, then Line AB sometimes intersects Segment CD.
2. If' two planes intersect, their intersection is always a line
3. If' a is perpendicular c and b perpendicular c, then a and b are sometimes parallel..
4. If two parallel planes are cut by a third plane, then the lines of' intersection are always coplanar..
5. A scalene triangle always has an acute angle.

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2. Two isosceles triangles with congruent bases are sometimes congruent.
3. Two isosceles triangles with congruent vertex angles are sometimes congruent.
4. Two equilateral triangles with congruent bases are always congruent.

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1. A square is always a rectangle.
3. A rhombus is sometimes a square.
2. A rectangle is sometimes a rhombus.
4. A rhombus is always a parallelogram.
5. A trapezoid sometimes has three congruent sides.
6. The diagonals of a trapezoid never bisect each other.
7. The diagonals of a rectangle are always congruent.
8. The diagonals of a parallelogram sometimes bisect the angles.

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A 1. If AX = XB, then X must be the midpoint of segment AB. False
2. Definitions may be used to justify statements in a proof. True
3. If a line and a plane are parallel, then the line is parallel to every line inthe plane. False
4. When two parallel lines are cut by a transversal, any two angles fbrmedare either congruent or supplementary. True
5. If' the sides of' one triangle are congruent to the corresponding sides of'another triangle, then the corresponding angles must also be congruent. True
6. Every isosceles trapezoid contains two pairs of congruent angles. True
7. If a quadrilateral has two pairs of supplementary angles, then it must be a parallelogram. False
8. If the diagonals of a quadrilateral bisect each other and are congruent, then the quadrilateral must be a square. False
9. In triangle PQR, m<P = m<R 50, If T lies on segment PR and rn<PQT 42,then PT < TR. False
10. In quad WXYZ, if WX = XY 25, YZ 20, ZW 16, and WY 20, then segment WY divides the quadrilateral into two similar triangles. True
11. Two equiangular hexagons are always similar. False

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1. If a conditional is false, then its converse is sometimes false.
2. Two vertical angles are never adjacent.
3. An angle sometimes has a complement.
4. Two parallel lines are always coplanar.
5. Two perpendicular lines are never both parallel to a third line.
6. A scalene triangle is never equiangular.
7. A regular polygon is always equilateral.
8. A rectangle is sometimes a rhombus.
9. fI Segment RS is congruent to Segment MN, Segment ST is congruent to Segment NO, and <R is congruent to <M, then triangles RST and MNO are sometimes congruent.
10. The HL method is never appropriate for proving that two acute triangles are congruent. (HL only works for right triangles)
11. If. AX = BX, AY BY, and points A, B, X, and Y are coplanar, then segment AB and segment XY are always perpendicular.
12. The diagonals of a trapezoid are sometimes perpendicular
13. If a line parallel to one side of a triangle intersects the other two sides, then the triangle formed is always similar to the given triangle
14. If triangle JKL is congruent to triangle NET and segment NE is perpendicular to segment ET, then it is never true that LJ < TE
15. If AB + BC > AC, then A, B, and C are sometimes collinear points
16. A triangle with sides of length x - 1, x , and x is never an obtuse triangle