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.
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
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.
6. given: /_f is supplementary to /_g and /_g is supplementary to /_h.
conjecture: /_f is supplementary to /_h.
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
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.
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.
19. given: a concave polygon
conjecture: it can be regular or irregular.
b. false; a concave polygon has an odd number of sides.
First you write the equation 2(2x-4)=28 because if b is the midpoint then AB is half of the line so you multiply that half by two the make it equal to the whole line.
Then you distribute the two and get 4x-8=28.
Then you add 8 to 28 and get 36.
Then you divide 36 by 4 because the 4 and x are being multiplied together so you have to divide to get them apart.
So then you get x=9 and you aren't done yet because you have to plug x into 2x-4.
So it is 2(9)-4 which is 18-4 which equals 14.
BC = 27
The point B is the midpoint of AC
=> AB = BC
=> 4x - 5 = 11 + 2x
Let's calculate x to work out BC
Transferring the components containing x to the left side, and other components to the right side:
=> 4x - 2x = 11 + 5
Simplifying both sides:
=> 2x = 16
=> x = 8
Working out BC:
=> BC = 11 + 2x = 11 + 2(8) = 11 + 16 = 27
Hope this helps!
oof tough question
sorry i can't ya : c gl tho
this shows a reflection over the x-axis and is translated one unit down and 6 units to the right (x + 6, y - 1)
hope this !
~just a girl in love with shawn mendes