# 3.1: Conditional Statements

## Problem 1 – Slopes of lines

Open a new *Cabri Jr*. file for each part (, , and ).

A. Construct a line and a point not on the line. Construct a second line through the point that is parallel to the first line. Find the slopes of both lines.

If two lines are parallel, then the slopes of the lines are ______________

*Converse:* ______________________________

*Inverse:* _______________________________

*Contrapositive:* _____________________________

Determine whether the above conditional statements are true or false. If you decide a statement is false, sketch a counterexample.

B. Construct a line and a point not on the line. Construct a second line through the point that is perpendicular to the first line. Find the slopes of both lines.

If two lines are perpendicular, then the slopes of the lines are ______________

*Converse:* ______________________________

*Inverse:* _______________________________

*Contrapositive:* _____________________________

Determine whether the above conditional statements are true or false. If you decide a statement is false, sketch a counterexample.

C. Construct two lines that have the same intercept.

If two different lines have the same intercept, then the lines have different slopes.

*Converse:* ______________________________

*Inverse:* ______________________________

*Contrapositive:* ______________________________

Determine whether the above conditional statements are true or false. If you decide a statement is false, sketch a counterexample.

## Problem 2 – Collinear and noncollinear segments

A. Use the *Cabri Jr*. file **COLSEG** to complete the following.

Find the distances , , and . Drag the points to create different lengths.

When do the lengths and add up to equal ? __________________

Write a conditional statement to express your conclusion:

If __________________ , then __________________

B. Use the *Cabri Jr*. file **NOCOLSEG** to complete the following.

Now explore what happens if , , and are not collinear.

What is the relationship between and ? _________________

Write a conditional statement to express your conclusion:

If __________________ , then __________________