Chapter 2: Q3 (page 49)

Use the conditional: If $\bar{A B}$ and $\bar{C D}$ intersect, then $\vec{A B}$ and $\vec{C D}$ intersect.
Rewrite the following pair of conditionals as a biconditional:
$\bar{A B} ≅ \bar{C D}$ if $A B = C D$ ; $\bar{A B} ≅ \bar{C D}$ only if $A B = C D$ .

Short Answer

Expert verified

The answer for the provided statement is $\bar{A B} ≅ \bar{C D}$ if and only if $A B = C D$ .

Step by step solution

Step 1. Observe the given symbols.

The symbols represent the condition that is for two segments that $\bar{A B} ≅ \bar{C D}$ when $A B = C D$ .

Step 2. Identify the biconditional.

Biconditional of the provided conditional will be the regeneration of it with a set of words which are “if and only if” so write the biconditional that is: $\bar{A B} ≅ \bar{C D}$ if and only if $A B = C D$ .

Step 3. State whether the biconditional is true or not.

There is no difference between the original conditional and the biconditional so the biconditional is true.

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Use the conditional: If $\bar{A B}$ and $\bar{C D}$ intersect, then $\vec{A B}$ and $\vec{C D}$ intersect.
Rewrite the following pair of conditionals as a biconditional:
$\bar{A B} ≅ \bar{C D}$ if $A B = C D$ ; $\bar{A B} ≅ \bar{C D}$ only if $A B = C D$ .

Short Answer

Step by step solution

Step 1. Observe the given symbols.

Step 2. Identify the biconditional.

Step 3. State whether the biconditional is true or not.

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Use the conditional: If AB¯and CD¯intersect, then AB→and CD→intersect.Rewrite the following pair of conditionals as a biconditional:AB¯≅CD¯if AB=CD; AB¯≅CD¯only if AB=CD.

Short Answer

Step by step solution

Step 1. Observe the given symbols.

Step 2. Identify the biconditional.

Step 3. State whether the biconditional is true or not.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

Use the conditional: If $\bar{A B}$ and $\bar{C D}$ intersect, then $\vec{A B}$ and $\vec{C D}$ intersect.
Rewrite the following pair of conditionals as a biconditional:
$\bar{A B} ≅ \bar{C D}$ if $A B = C D$ ; $\bar{A B} ≅ \bar{C D}$ only if $A B = C D$ .