2.1 - 2.3 Review

Conjecture

100

Triangle ABC is an equilateral triangle. Make a conjecture. 

<A = <B = <C

BA = CB = AB

200

Points A, B, and C are noncollinear and AC = CB = AB. Make a conjecture. 

It is an equilateral triangle 

300

Line segment AB bisects line segment XY at Z. Make a conjecture. 

<AZX is congruent to <AZY 

400

P, Q, R, and S are noncollinear and PQ = QR = RS = SP. Make a conjecture. 

The segments form a square or rhombus. 

500

<ABC is a right angle. Make a conjecture. 

Ray BA is perpendicular to ray BC. 

Inductive Reasoning

100

Find the next item in the sequence. 

5, -10, 15, -20 

25

200

Find the next item in the sequence.

-2, 1, -1/2, 1/4, -1/8

1/16

300

Find the next item in the sequence.

12, 6, 3, 1.5, 0.75

0.375

400

Find the next item in the sequence.

1, 6/5, 7/5, 8/5

9/5

500

Find the next item in the sequence.

1, 3, 9, 27, 81

243

If-Then Statements

100

Identify the hypothesis of the statement, If you live in Chicago, then you live in Illinois.

You live in Chicago 

200

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. 

300

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 

400

Write the statement in if-then form: All apes love bananas. 

If an animal is an ape, then it loves bananas. 

500

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. 

Counterexamples

100

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

200

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. 

300

Determine whether the conditional is true or false. If false, find a counterexample. 

If a is positive, then 10a is greater than a. 

True 

400

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. 

500

If a and b are negative, then a - b is also negative. 

False, if a=-2 and b=-3, then a - b = 1 

Converse

100

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. 

200

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.

300

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. 

400

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. 

500

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.