Geomentry Test

Which statement is a counterexample for the following conditional: If you live in Springfield, then you live in Illinois. A. Sara Lucas lives in Springfield B. Erin Naismith lives in Springfield, Massachusetts C. Billy lives in Chicago, Illinois D. Jonah lives in Springfield, Illinois

B

The part of a conditional that follows the then is what?

Conclusion

What is another name for an "if-then" statement?

Conditional

Every conditional has two parts. The part following the if is the ?

Hypothesis

What is the hypothesis and conclusion of this conditional statement: If two lines intersect at right angles, then the two lines are perpendicular

Hypothesis: Two lines intersect at right angles. Conclusion: Two lines lines are perpendicular

Write this statement as a conditional in if-then form: All triangles have three sides

If the figure is a triangle, then it has three sides.

Write the converse of the statement. If the converse is true, write true; if not true, provide a counterexample. If x = 4, then x2 = 16.

If x2 = 16, then x = 4. False; if x2 = 16, then x can be equal to -4.

A conditional can have a _____ of true or false?

Truth value

When a conditional and its converse are true, you can combine them as a true ____. a. counterexample b. biconditional c. unconditional d. hypothesis

b. biconditional

What is the converse of the following conditional? If a point is in the first quadrant, then its coordinates are positive. a. If a point is in the first quadrant, then its coordinates are positive. b. If a point is not in the first quadrant, then the coordinates of the point are not positive. c. If the coordinates of a point are positive, then the point is in the first quadrant. d. If the coordinates of a point are not positive, then the point is not in the first quadrant.

c. If the coordinates of a point are positive, then the point is in the first quadrant.

Is the statement a good definition? If not, find a counterexample. A square is a figure with two pairs of parallel sides and four right angles. a. The statement is a good definition. b. No; a rhombus is a counterexample. c. No; a rectangle is a counterexample. d. No; a parallelogram is a counterexample.

c. No; a rectangle is a counterexample.

Which conditional has the same truth value as its converese a. x=17, then |x| = 7 b. if a figure is a square, then it has four sides c. if x - 17 = 4 then x = 21 d. If an angle has measure 80, then it is acute

c. if x - 17 = 4 then x = 21

you can go to the movies if and only you do your homework conditional converese

conditional - if you can go to the movies then you did your homework converse - if you do your homework then you can go to the movies

If angles are congruent then they have equal measures] converese inverse

converese- if angles have equal measures then they are congruent bi - angles are congruent if they have equal measures

Which biconditional is NOT a good definition? a. A whole number is odd if and only if the number is not divisible by 2. b. An angle is straight if and only if its measure is 180. c. A whole number is even if and only if it is divisible by 2. d. A ray is a bisector of an angle if and only if it splits the angle into two angles.

d. A ray is a bisector of an angle if and only if it splits the angle into two angles.

Determine whether the conditional and its converse are both true. If both are true, combine them as a biconditional. If either is false, give a counterexample. If two lines are parallel, they do not intersect. If two lines do not intersect, they are parallel. a. One statement is false. If two lines do not intersect, they could be skew.. b. One statement is false. If two lines are parallel, they may intersect twice. c. Both statements are true. Two lines are parallel if and only if they do not intersect. d. Both statements are true. Two lines are not parallel if and only if they do not intersect.

d. Both statements are true. Two lines are not parallel if and only if they do not intersect.

What is the converse and the truth value of the converse of the following conditional? If an angle is a right angle, then its measure is 90. a. If an angle is not a right angle, then its measure is 90. False b. If an angle is not a right angle, then its measure is not 90. True c. If an angle has measure 90, then it is a right angle. False d. If an angle has measure 90, then it is a right angle. True

d. If an angle has measure 90, then it is a right angle. True

Decide whether the following definition of perpendicular is reversible. If it is, state the definition as a true biconditional. Two lines that intersect at right angles are perpendicular. a. The statement is not reversible. b. Reversible; if two lines intersect at right angles, then they are perpendicular. c. Reversible; if two lines are perpendicular, then they intersect at right angles. d. Reversible; two lines intersect at right angles if and only if they are perpendicular.

d. Reversible; two lines intersect at right angles if and only if they are perpendicular.

What is the conclusion of the following conditional? A number is divisible by 3 if the sum of the digits of the number is divisible by 3. a. The number is odd. b. The sum of the digits of the number is divisible by 3. c. If the sum of the digits of a number is divisible by 3, then the number is divisible by 3. d. The number is divisible by 3.

d. The number is divisible by 3.

One way to show that a statement is NOT a good definition is to find a ____. a. converse b. conditional c. biconditional d. counter example

d. counter example