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

Page 34

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

Page 75

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.

Page 77

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.

Page 96

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.

Page 114

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.

Page 151

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.

Page 199

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.

Page 281

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

Page 282

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

## Page 30

17. It is possible to locate three points in such a position that an unlimited number of' planes contain all three points.True18. It is possible for two intersecting lines to be noncoplanar.

False19. Through any three points there is at least one line.

False20. If points A and B lie in plane P, then so does any point of Ray AB.

True## Page 34

12. If today is Friday, then tomorrow is Saturday.True13. If x > 0, then x2 > 0.

False14. If a number is divisible by 6, then it is divisible by 3.

True15. If 6x=18 then x=3

3.

True## Page 75

15. Two skew lines areneverparallel.16. Two parallel lines are

alwayscoplanar.17. A line in the plane of the ceiling and a line in the plane of' the floor are

sometimesparallel.18. Two lines in the plane of' the floor are

neverskew.19. A line in the plane of' a wall and a line in the plane of' the floor are

a.

sometimesparallel. b.sometimesintersecting. c.sometimesskew.## Page 77

30. When there is a transversal of two lines, the three lines arealwayscoplanar.31. Three lines intersecting in one point are

sometimescoplanar.32. Two lines that are not coplanar

neverintersect.33. Two lines parallel to a third line are

alwaysparallel to each other.34. Two lines skew to a third line are

sometimesskew to each other.35. Two lines perpendicular to a third line are

sometimesperpendicular to each other.36. Two planes parallel to the same line are

sometimesparallel to each other.37. Two planes parallel to the same plane are

alwaysparallel to each other.38. Lines in two parallel planes are

sometimesparallel to each other.39. Two lines parallel to the same plane are

sometimesparallel to each other.## Page 96

1. If' a triangle is isosceles, then it issometimesequilateral.2. If a triangle is equilateral, then it is

alwaysisosceles3. If a triangle is scalene, then it is

neverisosceles.4. If a triangle is obtuse, then it is

sometimesisosceles.## Page 114

1. If' Line AB intersects Segment CD, then Line ABsometimesintersects Segment CD.2. If' two planes intersect, their intersection is

alwaysa line3. If'

ais perpendicularcandbperpendicularc, thenaandbaresometimesparallel..4. If two parallel planes are cut by a third plane, then the lines of' intersection are

alwayscoplanar..5. A scalene triangle

alwayshas an acute angle.## Page 151

2. Two isosceles triangles with congruent bases aresometimescongruent.3. Two isosceles triangles with congruent vertex angles are

sometimescongruent.4. Two equilateral triangles with congruent bases are

alwayscongruent.## Page 199

1. A square isalwaysa rectangle.3. A rhombus is

sometimesa square.2. A rectangle is

sometimesa rhombus.4. A rhombus is

alwaysa parallelogram.5. A trapezoid

sometimeshas three congruent sides.6. The diagonals of a trapezoid

neverbisect each other.7. The diagonals of a rectangle are

alwayscongruent.8. The diagonals of a parallelogram

sometimesbisect the angles.## Page 281

A 1. If AX = XB, then X must be the midpoint of segment AB.False2. Definitions may be used to justify statements in a proof.

True3. If a line and a plane are parallel, then the line is parallel to every line inthe plane.

False4. When two parallel lines are cut by a transversal, any two angles fbrmedare either congruent or supplementary.

True5. If' the sides of' one triangle are congruent to the corresponding sides of'another triangle, then the corresponding angles must also be congruent.

True6. Every isosceles trapezoid contains two pairs of congruent angles.

True7. If a quadrilateral has two pairs of supplementary angles, then it must be a parallelogram.

False8. If the diagonals of a quadrilateral bisect each other and are congruent, then the quadrilateral must be a square.

False9. In triangle PQR, m<P = m<R 50, If T lies on segment PR and rn<PQT 42,then PT < TR.

False10. In quad WXYZ, if WX = XY 25, YZ 20, ZW 16, and WY 20, then segment WY divides the quadrilateral into two similar triangles.

True11. Two equiangular hexagons are always similar.

False## Page 282

1. If a conditional is false, then its converse issometimesfalse.2. Two vertical angles are

neveradjacent.3. An angle

sometimeshas a complement.4. Two parallel lines are

alwayscoplanar.5. Two perpendicular lines are

neverboth parallel to a third line.6. A scalene triangle is

neverequiangular.7. A regular polygon is

alwaysequilateral.8. A rectangle is

sometimesa 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

sometimescongruent.10. The HL method is

neverappropriate 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

alwaysperpendicular.12. The diagonals of a trapezoid are

sometimesperpendicular13. If a line parallel to one side of a triangle intersects the other two sides, then the triangle formed is

alwayssimilar to the given triangle14. If triangle JKL is congruent to triangle NET and segment NE is perpendicular to segment ET, then it is

nevertrue that LJ < TE15. If AB + BC > AC, then A, B, and C are

sometimescollinear points16. A triangle with sides of length x - 1, x , and x is

neveran obtuse triangle