# 3.1: Conditional Statements

Difficulty Level: At Grade Created by: CK-12

## Problem 1 – Slopes of lines

Open a new Cabri Jr. file for each part (\begin{align*}A\end{align*}, \begin{align*}B\end{align*}, and \begin{align*}C\end{align*}).

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 \begin{align*}y-\end{align*}intercept.

If two different lines have the same \begin{align*}y-\end{align*}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 \begin{align*}AB\end{align*}, \begin{align*}BC\end{align*}, and \begin{align*}AC\end{align*}. Drag the points to create different lengths.

\begin{align*}& AB \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AB + BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;}\\ & AB \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AB + BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;}\\ & AB \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AB + BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

When do the lengths \begin{align*}AB\end{align*} and \begin{align*}BC\end{align*} add up to equal \begin{align*}AC\end{align*}? __________________

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 \begin{align*}AB\end{align*}, \begin{align*}BC\end{align*}, and \begin{align*}AC\end{align*} are not collinear.

\begin{align*}& AB \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AB + BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;}\\ & AB \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AB + BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;}\\ & AB \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AB + BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

What is the relationship between \begin{align*}AB + BC\end{align*} and \begin{align*}AC\end{align*}? _________________

Write a conditional statement to express your conclusion:

If __________________, then __________________

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