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Example 2: Identify the hypothesis and conclusion of each statement. Then write each statement in if-then form.

Two lines that are perpendicular form right angles.

Short Answer

Expert verified

The hypothesis is 鈥渢wo lines are perpendicular鈥 and the conclusion is 鈥渢hey form right angles鈥. The required if-then statement is 鈥淚f two lines are perpendicular, then they form right angles.鈥

Step by step solution

01

Step 1. State the concept.

In a conditional statement, the independent part is the hypothesis and the dependent part is the conclusion.

In an if-then statement, the part of the statement immediately following 鈥渋f鈥 is the hypothesis, and the part of the statement immediately following 鈥渢hen鈥 is the conclusion.

02

Step 2. List the given data.

The given statement is 鈥淭wo lines that are perpendicular form right angles鈥.

03

Step 3. Identify the hypothesis and conclusion.

The given statement has two parts, 鈥渢wo lines are perpendicular鈥 and 鈥渢hey form right angles鈥.

Note that two lines forming a right angle depend on the line being perpendicular.

So, 鈥渢wo lines are perpendicular鈥 is the independent part of the statement and thus, the hypothesis. Similarly, 鈥渢hey form right angles鈥 is the dependent part of the statement and thus, the conclusion.

04

Step 4. Rewrite as an if-then statement.

Write the hypothesis after 鈥渋f鈥 and conclusion after 鈥渢hen鈥 in an if-then statement to get:

鈥淚f two lines are perpendicular, then they form right angles.鈥

This is the required if-then statement.

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