We all want Equality
Name the Property of Equality that states: For any segment AB, AB=AB.
Reflexive Property of Equality
Rewrite in the conditional form:
All birds have feathers.
If it is a bird, then it has feathers.
Name the definition, theorem, or postulate that leads to the conclusion:
Given: A picture that shows two adjacent angles, <1 and <2, that have a sum of 180 degrees.
Conclusion: m<1 + m<2 = 180
Definition of Linear Pair
OR
Definition of Supplementary
If the product of two numbers is positive, then the two numbers must also be positive.
-5 x -3 =15
(any example that shows multiplying two negative numbers to get a positive number; or a negative number and 0)
Use the Law of Detachment if possible:
If it is someone's birthday, then he/she will eat cake. It is not Drew's birthday.
No conclusion. The hypothesis was not satisfied.
Write the converse:
If you studied, then you passed.
If you passed, then you studied.
Name the definition, theorem, or postulate that leads to the conclusion:
Given: BD bisects AM at point Q.
Conclusion: AQ = QM
Definition of Bisect
The sum of one positive and one negative is always a positive.
-7 + 5 = -2
(anything that shows adding a negative and a positive number to get a negative sum)
Use the Law of Detachment if possible.
If it is sunny out, then dogs will be at the dog park. It is sunny out.
Dogs will be at the dog park.
Name the PoE that states: For any segments AB, CD, and EF, if AB=CD and CD=EF, then AB=EF
Transitive Property of Equality
Give the converse of the conditional statement. If the converse is true, write it as a true biconditional. If it is false, give a counterexample.
If it is a zebra, then it has stripes.
Converse: If it has stripes, then it is a zebra.
False. Counterexample: Tiger (anything with stripes)
Name the definition, theorem, or postulate:
If 3 points, A, B, and C are collinear, then
AB + BC = AC.
Segment Addition Postulate
All quadrilaterals are equilateral.
rectangle
(Parallelogram, Kite, etc. Could just be a four sided polygon where all side lengths are different)
Use the Law of Syllogism if possible.
If Maia goes to sleep at a decent time, then she feels well rested. If she feels well rested, then she will ace her geometry test.
If Maia goes to sleep at a decent time, then she will ace her geometry test.
Name the Property of Equality used. If 5x=30, then x=6.
Division Property of Equality
Is the following a "good definition"? Explain why or why not.
A complementary angle pair has a sum of 90 degrees.
Yes. It is a good definition because both the conditional and the converse are true (it is reversible).
Name the definition, theorem, or postulate that leads to the conclusion:
Given: <1 and <2 are vertical angles.
Conclusion: m<1 = m<2
Definition of Vertical Angles
OR
Vertical Angles Theorem
All shapes are polygons
circle
(anything with curves)
Use the Law of Syllogism if possible.
If Cade has his Driver's License, then he can drive to school. If Cade has his Driver's License, then you can hear his keys.
No conclusion. The repeated portions were both the hypothesis.
Is the following a "good definition"? Explain why or why not.
An acute angle is made up of two rays that share an endpoint.
Not a good definition. The converse is false (it is not reversible). Counterexample: obtuse angle (or any other angle)
Name the definition, theorem, or postulate:
If <ABC and <CBD are adjacent, then <ABC + <CBD = <ABD.
Angle Addition Postulate
All pentagons are convex.
Would have to draw an image of a pentagon that is concave.
Use the Law of Detachment and the Law of Syllogism if possible to make a conclusion.
If students do well on the Logic Test, then Ms. Garroutte will dance a jig. If Ms. Garroutte dances a jig, then she will pull a muscle.
The students do well on the Logic Test.
Ms. Garroutte will pull a muscle.