Question

of each conditional statement.

1. \if there is no struggle, there is no progress.\ (frederick douglass)
2. if two angles are adjacent, then they have a common side.
3. if you lead, then i will follow.
4. if $3x - 4 = 11$, then $x = 5$.
5. if two angles are vertical, then they are congruent.

Explanation:

Step1: Recall the definition of a conditional statement

A conditional statement is in the form "If \( p \), then \( q \)", where \( p \) is the hypothesis and \( q \) is the conclusion. To identify the hypothesis and conclusion, we look at the parts of the statement: the hypothesis is the part following "If" and the conclusion is the part following "then".

Step2: Analyze each statement

Statement 7: "If there is no struggle, there is no progress." (Frederick Douglass)

• Hypothesis (\( p \)): There is no struggle
• Conclusion (\( q \)): There is no progress

Statement 8: If two angles are adjacent, then they have a common side.

• Hypothesis (\( p \)): Two angles are adjacent
• Conclusion (\( q \)): They have a common side

Statement 9: If you lead, then I will follow.

• Hypothesis (\( p \)): You lead
• Conclusion (\( q \)): I will follow

Statement 10: If \( 3x - 4 = 11 \), then \( x = 5 \).

• Hypothesis (\( p \)): \( 3x - 4 = 11 \)
• Conclusion (\( q \)): \( x = 5 \)

Statement 11: If two angles are vertical, then they are congruent.

• Hypothesis (\( p \)): Two angles are vertical
• Conclusion (\( q \)): They are congruent

Answer:

For each conditional statement:

1. Hypothesis: There is no struggle; Conclusion: There is no progress
2. Hypothesis: Two angles are adjacent; Conclusion: They have a common side
3. Hypothesis: You lead; Conclusion: I will follow
4. Hypothesis: \( 3x - 4 = 11 \); Conclusion: \( x = 5 \)
5. Hypothesis: Two angles are vertical; Conclusion: They are congruent