Q

#### Reasoning and Proof

(10 Questions)Helps us understand postulates about points, lines, and planes.

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Use the Law of Syllogism select a word which makes the concluding statement true. The Oak Terrace apartment building does not allow dogs. Serena lives at Oak Terrace.
So Serena ( must, may, may not ) keep a dog.

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\angle 1 and \angle 2 are supplementary, \angle 3 and \angle 4 are supplementary . m\angle 3+m \angle 4 = m\angle 1 + m \angle 2 because of -------------------- property

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In a picture frame, the corners are all right angles, m\angle1 = m\angle2 = 52^\circ. \angle 4\cong \angle 3 because of congruent ---------------- theorem.

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Using the Law of Detachment state whether the argument is valid. If the measures of two angles are 90^\circ, then the two angles are complementary. Because m\angleA+m\angleC = 90^\circ, \angle A and \angleC are complementary. This is true because of the law of detachment. Now using the Law of Detachment answer if this argument is valid. If two adjacent angles form a right angle then the two angles are complementary. Because \angle A and \angle C are complementary they are adjacent.

**A**

**B**

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A biconditional statement is a statement that contains the phrase "if and only if". Determine which biconditional statement related to the diagram is true

**A**

**B**

**C**

**D**

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Donald received a 6% pay increase at work and his new wage is $12.72. Find Donald's old wage by using the algebraic properties of equality. The formula c( r + 1) n where c is the current wage in dollars per hour, r is the percent increase and n is the new wage can be used to do so. The old wage of Donald is ------------ dollars. Answer it as a number.

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Read the question and answer this:

**A**

**B**

**C**

**D**

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Logic does not exist in cartoons. Deductive reasoning uses facts, definitions and accepted properties in a logical order to write a logical argument. This differs from inductive reasoning which is used to form a conjecture. There are two laws of deductive reasoning - The Law of Detachment and the Law of Syllogism.
If p\rightarrow q is a true conditional statement and p is true then q is true is the LAW OF DETACHMENT.
If p\rightarrow q and q\rightarrow r are true conditional statements then p\rightarrow r is true is the LAW OF SYLLOGISM.
Please enter Duh to move to the next question.

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A conditional statement has two parts - a hypothesis and a conclusion. An example is given in the picture shown. The measure of a right angle is 90^\circ can be written as a conditional statement by adding if and then. If the measure of an angle is 90^\circ then it is a right angle. Rewrite the conditional statement in an if-then form. Hagfish live in salt water.

**A**

**B**

**C**

**D**

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When you negate the hypothesis and the conclusion of a conditional statement, you form the inverse. When you negate the hypothesis and conclusion of the converse of a conditional statement, you form the contrapositive. A conditional statement is " If the measure of an angle is 44^\circ, then the angle is acute". Which of the following is true?
I. The statement is true
II. The converse of the statement is true.
III. The contrapositive of the statement is true.

**A**

**B**

**C**

**D**

by Sangeetha Pulapaka