Show:
conditionals & conjecture
proofs
Converse, inverse & contrapositive
Laws of Deduction
Ch 1
100
Provide a counter example showing the conjecture is false: "If angle A and angle B are supplementary then angle A = 90­­° and angle B = 90°
What is angle A = 50 and angle B = 130
100
What reason justifies the statements: angle 1 and angle 2 are supplementary angle 1 + angle 2 = 180°
What is definition of supplementary angles
100
This is the converse of the statement: If 3 points are on a line then they are collinear.
What is If 3 points are collinear then they are on a line.
100
What is a logical conclusion to the following statements. If a figure is a square then it is a quadrilateral. If a figure is a quadrilateral then it is a polygon.
What is If a figure is a square then it is a polygon.
100
Find the length of segment AB if A(3, 4) and B(-5, 6).
What is 8.2
200
Write the statement as a conditional and determine its truth value. An angle less than 90° is an acute angle.
What is If an angle is less than 90° then it is an acute angle. true.
200
This reason justifies the following statements: ray AB bisects angle CAD angle CAB = angle BAD
What is definition of angle bisectors
200
For the conditional statement give both its inverse and its contrapositive. If a dog has fleas then it scratches its skin.
What is inverse: If a dog doesn't have fleas then it doesn't scratch its skin. contrapositive: If a dog doesn't scratch its skin then it doesn't have fleas.
200
angles A + angle B = 180°. If two angles add to 180° then they are supplementary. What conclusion can be made?
What is angles A and angles B are supplementary
200
B is midpoint of CX Find B if C(2, 5) and X(-1, 2)
What is (.5, 3.5)
300
Determine if conjecture is true or false. Conjecture: If AB = BC then B is the midpoint.
What is false. Could be two congruent sides of an angle.
300
This reason justifies the statements: AC = AB and AC = CD AB = CD
What is substitution or What is the transitive property
300
Give the contrapositive of the statement: All triangles are polygons.
What is If a figure is not a polygon then it is not a triangle.
300
The measure of angle 1 = 5x + 10, the measure of angle 2 = 15x + 20, If angle 1 and angle 2 are complementary what is the measure of angle 2.
What is 65°
400
Write the statement as a conditional. Complementary angles are angles that add to 90°
What is If angles are complementary then they add to 90°
400
What reason justifies the statement: angle 1 and angle 2 form a linear pair angle 1 and angle 2 are supplementary
What is linear pair theorem
400
This statement is logically equivalent to the statement: If an angle is not less than 90° then it is not acute.
What is If an angle is acute then it is less than 90°
400
If an animal is a cat then it is a feline. If an animal is a feline then it is a carnivore. conclusion: If an animal is not a carnivore then it is not a cat. Is this conclusion valid? Why or why not.
What is yes, because it is the contrapositive of the original conclusion
400
Find the coordinate for A if B is midpoint of AC and B(0, 5) and C(-4, 2)
What is (4, 8)
500
Write the conditional for the given inverse statement and determine it truth value.. "If angles are not congruent then they are not vertical.
What is If angles are congruent then they are vertical. False, right angles are congruent but not vertical.
500
Which reason justifies the following statements: B is midpoint of AC AB = BC
What is definition of midpoint
500
Which statement flips the conditional statement.
What is the converse
500
If two angles add to 90° then they are complementary. Angle A + angle B = 90°. What conclusion can be made.
What is Angle A and Angle B are complementary.
500
Ray BD bisects angle ABC. If angle ABD = 4x + 15 and angle CBD = 7x - 3, find the measure of angle ABD.
What is 39°