Determine whether the conjecture is true or false. give a counterexample for any false conjecture.
1. given: points a, b,c and d
conjecture: a, b,c and d are coplanar.
a. true
b. false; the four points do not have to be in a straight line.
c. false; two points are always coplanar but four are not.
d, false; three points are always coplanar but four are not.

3. given: m^2 + 6 = 10
conjecture: m = 2
a. false; m = 14
b. true
c. false; m = 3
d. false; m = -2 or m = 2

4. given: two angles are supplementary.
conjecture: they are both acute angles.
a. false; either both are right or one is obtuse.
b. false; either both are right or they are adjacent.
c. false; they must be vertical angles.
d. true

6. given: /_f is supplementary to /_g and /_g is supplementary to /_h.
conjecture: /_f is supplementary to /_h.
a. true
b. false; they could be vertical angles.
c. false; they could be right angles.
d. false; they could be non-right congruent angles.

10. given: point b is in the interior of /_adc
conjecture: /_adb≅ /_bdc
a. true
b. false; m/_adb + m/_bdc = 90.
c. false; just because it is in the interior does not mean it is on the bisecting line.
d. false; m/_adb may be obtuse

16. given: /_abc, /_dbe are coplanar.
conjecture: they are vertical angles.
a. false; one angle may be in the interior of the other.
b. true.
c. false; they angles may be adjacent.
d. false; the angles may be supplementary.

18. given: segments rt and st, twice the measure of st is equal to the measure of rt.
conjecture: s is the midpoint of segment rt.
a. false; st could be the segment bisector of rt.
b. false; lines do not have midpoints.
c. false; point s may not be on rt.
d. true

19. given: a concave polygon
conjecture: it can be regular or irregular.
a. true
b. false; a concave polygon has an odd number of sides.