Perpendicular lines intersect to form right angles. What is true about the statement? Check all that apply. A. The hypothesis is “if perpendicular lines.” B. The hypothesis is “if lines are perpendicular.” C. The conclusion is “then right angles.” D. This is a compound statement. E. This is a conditional statement.
The correct answer and explanation is:
Correct answers:
B. The hypothesis is “if lines are perpendicular.”
C. The conclusion is “then right angles.”
E. This is a conditional statement.
Explanation:
The statement “Perpendicular lines intersect to form right angles” can be rewritten in conditional form as “If lines are perpendicular, then they intersect to form right angles.” In this form, the “if” part is called the hypothesis, and the “then” part is called the conclusion.
Option B correctly identifies the hypothesis. The hypothesis describes the condition being tested or assumed. Here, the hypothesis is “if lines are perpendicular.” Option A is incorrect because it is less precise and uses “if perpendicular lines,” which is not the full hypothesis form.
Option C correctly identifies the conclusion. The conclusion is the outcome or result that follows from the hypothesis. In this case, it is “then right angles,” meaning the lines form right angles when they are perpendicular.
Option E is also correct because the statement is a conditional statement. A conditional statement has the form “if… then…” expressing a cause and effect or a logical connection between two parts. This is exactly what the given statement is.
Option D is incorrect because the statement is not a compound statement. Compound statements involve combining two or more statements using connectors like “and,” “or,” or “but.” The statement about perpendicular lines is a simple conditional statement, not a combination of multiple statements.
In summary, the statement is a conditional statement with a clear hypothesis (“if lines are perpendicular”) and conclusion (“then right angles”). Understanding these parts helps in logical reasoning and in geometry proofs.