Properties, Postulates, & Theorems Conditionals, Biconditionals, Etc. Deductive Reasoning Algebraic Reasoning Proofs

Properties, Postulates, & Theorems 100 Why does

Properties, Postulates, & Theorems 100 Distributive Property

If BY = XD and XD = ZC then why does BY = ZC? Properties, Postulates, & Theorems 200

Transitive Property Properties, Postulates, & Theorems 200

Properties, Postulates, & Theorems 300 Directions: Determine if the following is always, sometimes, or never true. Vertical angles are supplementary.

Properties, Postulates, & Theorems 300 Sometimes. (Only when perpendicular lines.)

Properties, Postulates, & Theorems 400 Directions: Determine if the following is always, sometimes, or never true. Every obtuse angle has a supplement.

Properties, Postulates, & Theorems 400 Always.

Properties, Postulates, & Theorems 500 Directions: Determine if the following is always, sometimes, or never true. Adjacent angles form linear pairs.

Properties, Postulates, & Theorems 500 Sometimes. (If the two angles are supplementary.)

Conditionals, Biconditionals, etc. 100 Identify the hypothesis and conclusion of the following statement: If two lines intersect at right angles, then the two lines are perpendicular.

Conditionals, Biconditionals, etc. 100 Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are perpendicular.

Conditionals, Biconditionals, etc. 200 Write the conditional and converse of the following: Exercising keeps you in good shape!

Conditionals, Biconditionals, etc. 200 Conditional: If you exercise, then you are in good shape. Converse: If you are in good shape, then you exercise.

Conditionals, Biconditionals, etc. 300 What two conditions make up the following biconditional: Two lines are perpendicular if and only if they intersect to form four right angles.

Conditionals, Biconditionals, etc. 300 If two lines are perpendicular then, they intersect to form four right angles. If two lines form four right angles, then they are perpendicular.

Conditionals, Biconditionals, etc. 400 Write the converse. If the converse is true, then write the biconditional. If the converse is false, then write a counter example. If x = 3, then

Conditionals, Biconditionals, etc. 400 Converse: If, then x = 3 False. Counter example:

Conditionals, Biconditionals, etc. 500 Is the following a statement a good definition? Prove it. If not, find a counterexample. A ray that divides an angle into two congruent angles is an angle bisector.

Conditionals, Biconditionals, etc. 500 Conditional: If a ray divides an angle into two congruent angles, then it is an angle bisector. (True) Converse: If a ray is an angle bisector, then it divides an angle into two congruent angles. (True) Biconditional: A ray divides an angle into two congruent angles if and only if it is an angle bisector.

Deductive Reasoning 100 Use the Law of Detachment to draw a conclusion. If a team wins on Sunday, then practice is cancelled Monday. The Bears won on Sunday!

Deductive Reasoning 100 The Bears practice is cancelled on Monday!

Deductive Reasoning 200 Use the Law of Detachment to draw a conclusion. If the measure of two angles is 90 degrees, then they are complementary.

Deductive Reasoning 200 Angle A and Angle B are complementary

Deductive Reasoning 300 Use the Law of Syllogism to draw a conclusion. If you study, then you will earn an A. If you earn an A, then you are HAPPY!

Deductive Reasoning 300 If you study, then you are HAPPY!

Deductive Reasoning 400 Use the Law of Detachments to draw a conclusion. If a dog eats Doggie Delights, then it is a happy dog. Fido is a happy dog.

No Conclusion! Deductive Reasoning 400

Deductive Reasoning 500 Use the Law of Syllogism to draw a conclusion. If two lines intersect, then they intersect at a point. If two lines are not parallel, then they intersect.

Deductive Reasoning 500 If two lines are not parallel, then they intersect at a point.

Algebraic Reasoning 100 Justify each step: Given

Algebraic Reasoning 100 Given Addition Property of Equality Division Property of Equality

Algebraic Reasoning 200 The measure of two verticals angles are Solve for x. Justify each step.

Algebraic Reasoning 200

Algebraic Reasoning 300 A B C O Given: Prove:

A B C O Algebraic Reasoning 300 Angle Addition Post. Substitution Distributive Prop. Simplify. Addition Prop. Division Prop.

Algebraic Reasoning 400 Given: Prove:

Algebraic Reasoning 400 Given Substitution Multiplication Prop. of = Subtraction Prop. of = Division Prop. of =

Algebraic Reasoning 500 Solve for x and justify each step: Segment KL is bisected by point M,

Algebraic Reasoning 500 K M L Segment Addition Post. bisect  2 segments Substitution Simplify Subtraction Prop. of = Division Prop. of =

Proofs 100 Given: Prove: Statements Reasons A B C D

Proofs 100 Given: Prove: Statements Reasons A B C D

Proofs 200 Given: Prove: Statements Reasons H D GF E

Proofs 200 Given: Prove: Statements Reasons H D GF E

Proofs 300 Given: Prove: Statements Reasons UFN E G O

Proofs 300 Given: Prove: Statements Reasons U E F G O N

Proofs 400 Prove: Given: Statements Reasons A C B D

Proofs 400 Prove: Given: Statements Reasons A C B D

Proofs 500 Prove: Given: Statements Reasons

Proofs 500 Prove: Given: Statements Reasons