Questions: Select the statement that is the contrapositive of the following statement: If a ray cuts an angle into two smaller, congruent angles, then it is an angle bisector. Answer If a ray isn't an angle bisector, then it doesn't cut an angle into two smaller, congruent angles. If a ray is an angle bisector, then it cuts an angle into two smaller, congruent angles. If a ray cuts an angle into two smaller, congruent angles, then it Submit Answer isn't an angle bisector. If a ray doesn't cut an angle into two smaller, congruent angles, then it isn't an angle bisector.

Select the statement that is the contrapositive of the following statement:
If a ray cuts an angle into two smaller, congruent angles, then it is an angle bisector.

Answer

If a ray isn't an angle bisector, then it doesn't cut an angle into two smaller, congruent angles.

If a ray is an angle bisector, then it cuts an angle into two smaller, congruent angles.
If a ray cuts an angle into two smaller, congruent angles, then it
Submit Answer
isn't an angle bisector.

If a ray doesn't cut an angle into two smaller, congruent angles, then it isn't an angle bisector.

Transcript text: Select the statement that is the contrapositive of the following statement: If a ray cuts an angle into two smaller, congruent angles, then it is an angle bisector. Answer If a ray isn't an angle bisector, then it doesn't cut an angle into two smaller, congruent angles. If a ray is an angle bisector, then it cuts an angle into two smaller, congruent angles. If a ray cuts an angle into two smaller, congruent angles, then it Submit Answer isn't an angle bisector. If a ray doesn't cut an angle into two smaller, congruent angles, then it isn't an angle bisector.

Solution

Solution Steps

To find the contrapositive of a given statement, we need to negate both the hypothesis and the conclusion and then switch their places. The original statement is: "If a ray cuts an angle into two smaller, congruent angles, then it is an angle bisector."

Identify the hypothesis and conclusion:
- Hypothesis: A ray cuts an angle into two smaller, congruent angles.
- Conclusion: It is an angle bisector.
Negate both the hypothesis and the conclusion:
- Negated Hypothesis: A ray doesn't cut an angle into two smaller, congruent angles.
- Negated Conclusion: It isn't an angle bisector.
Switch the negated hypothesis and conclusion:
- Contrapositive: If a ray isn't an angle bisector, then it doesn't cut an angle into two smaller, congruent angles.

Step 1: Identify the Hypothesis and Conclusion

The original statement is: "If a ray cuts an angle into two smaller, congruent angles, then it is an angle bisector."

Hypothesis: A ray cuts an angle into two smaller, congruent angles.
Conclusion: It is an angle bisector.

Step 2: Negate Both the Hypothesis and Conclusion

Negate the hypothesis and the conclusion:

Negated Hypothesis: A ray doesn't cut an angle into two smaller, congruent angles.
Negated Conclusion: It isn't an angle bisector.

Step 3: Switch the Negated Hypothesis and Conclusion

Switch the places of the negated hypothesis and conclusion to form the contrapositive:

Contrapositive: If a ray isn't an angle bisector, then it doesn't cut an angle into two smaller, congruent angles.

Step 4: Match the Contrapositive with Given Statements

Compare the contrapositive statement with the given options:

If a ray isn't an angle bisector, then it doesn't cut an angle into two smaller, congruent angles.
If a ray is an angle bisector, then it cuts an angle into two smaller, congruent angles.
If a ray cuts an angle into two smaller, congruent angles, then it isn't an angle bisector.
If a ray doesn't cut an angle into two smaller, congruent angles, then it isn't an angle bisector.

The contrapositive statement matches the first option.