Geo Unit 4 part 2 Deductive Reasoning hw

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What is deductive reasoning?

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Deductive reasoning is a logical process where a conclusion is drawn from a set of premises that are generally assumed to be true. It involves applying general principles to specific cases.

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What is a conditional statement?

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A conditional statement is a logical statement that has two parts: a hypothesis (if part) and a conclusion (then part). It is often written in the form 'If P, then Q'.

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What is the transitive property in geometry?

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The transitive property states that if one quantity is equal to a second quantity, and the second quantity is equal to a third quantity, then the first quantity is equal to the third quantity.

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How do you write a conclusion from a conditional statement?

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To write a conclusion from a conditional statement, identify the hypothesis and conclusion, and if the hypothesis is true, then the conclusion must also be true.

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What is the relationship between a rhombus and a parallelogram?

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A rhombus is a specific type of parallelogram where all sides are of equal length. Therefore, all properties of parallelograms apply to rhombuses.

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What does it mean for angles to be congruent?

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Congruent angles are angles that have the same measure. In geometry, this means that they can be superimposed on each other.

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What is the conclusion if 'If A, then B' and 'If B, then C'?

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The conclusion is 'If A, then C', based on the transitive property of conditional statements.

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What is the significance of the hypothesis in a conditional statement?

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The hypothesis is the condition that must be met for the conclusion to be true. If the hypothesis is false, the truth of the conclusion cannot be determined.

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How can you determine if a statement is valid?

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A statement is valid if the conclusion logically follows from the premises. In deductive reasoning, if the premises are true, the conclusion must also be true.

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What is an example of a real-world application of deductive reasoning?

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An example is: If it rains, then the ground will be wet. It is raining. Therefore, the ground is wet.