Conjecture
Triangle ABC is an equilateral triangle. Make a conjecture.
<A = <B = <C
BA = CB = AB
Find the next item in the sequence.
5, -10, 15, -20
25
Identify the hypothesis of the statement, If you live in Chicago, then you live in Illinois.
You live in Chicago
Determine whether the following conjecture is true or false. Give a counterexample for any false conjecture.
If DE is perpendicular to EF, then <DEF is a right angle.
True
Write the converse to the statement: If two lines are perpendicular to the same line, then they are parallel.
If two lines are parallel, then they are perpendicular to the same line.
Points A, B, and C are noncollinear and AC = CB = AB. Make a conjecture.
It is an equilateral triangle
Find the next item in the sequence.
-2, 1, -1/2, 1/4, -1/8
1/16
Write the statement in if-then form.
A polygon with four sides is a quadrilateral.
If a polygon has four sides, then it is a quadrilateral.
Determine whether the following conjecture is true or false. Give a counterexample for any false conjecture.
If <ABC and <DEF are supplementary, then <ABC and <DEF form a linear pair.
False, the angles could be nonadjacent.
Write the converse to the statement: If an angle is acute, then its measure is less than 90.
If an angle measures less than 90, then it is acute.
Line segment AB bisects line segment XY at Z. Make a conjecture.
<AZX is congruent to <AZY
Find the next item in the sequence.
12, 6, 3, 1.5, 0.75
0.375
Identify the hypothesis and conclusion:
If the drama class raises $2000, then they will go on tour.
H: the drama class raises $2000
C: they will go on tour
Determine whether the conditional is true or false. If false, find a counterexample.
If a is positive, then 10a is greater than a.
True
Write the converse to the statement: If two angles are complementary, then the sum of their measures is 90.
If the sum of the measures of two angles is 90, then the angles are complementary.
P, Q, R, and S are noncollinear and PQ = QR = RS = SP. Make a conjecture.
The segments form a square or rhombus.
Find the next item in the sequence.
1, 6/5, 7/5, 8/5
9/5
Write the statement in if-then form: All apes love bananas.
If an animal is an ape, then it loves bananas.
Determine whether the conditional is true or false. If false, give a counterexample.
If Nemo is an orange cat, then James will get a 100 on his test.
True, if the hypothesis is false, the statement is always true.
Write the converse to the statement: If 89 is divisible by 2, then 89 is an even number. Then, determine if it is true or false, and if false, give a counterexample.
If 89 is an even number, then 89 is divisible by 2.
True, if the hypothesis is false, the conditional is true.
<ABC is a right angle. Make a conjecture.
Find the next item in the sequence.
1, 3, 9, 27, 81
243
Write the statement in if-then form: Adjacent angles share a common vertex and a common side.
If two angles are adjacent, then they share a common vertex and a common side.
If a and b are negative, then a - b is also negative.
False, if a=-2 and b=-3, then a - b = 1
Write the converse to the statement: If a polygon is a square, then it is a rectangle. Then, determine if it is true or false, and if false, give a counterexample.
If a polygon is a rectangle, then it is a square.
False, the sides could be different lengths.