Mathematics, 12.11.2019 04:31, makinzy03

# 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.

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Mathematics, 17.06.2020 18:57

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