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3.1: Conditional Statements

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Problem 1 – Slopes of lines

Open a new Cabri Jr. file for each part ($A$, $B$, and $C$).

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 $y-$intercept.

If two different lines have the same $y-$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 $AB$, $BC$, and $AC$. Drag the points to create different lengths.

$& AB \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AB + BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;}\\& AB \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AB + BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;}\\& AB \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AB + BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;}$

When do the lengths $AB$ and $BC$ add up to equal $AC$? __________________

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 $AB$, $BC$, and $AC$ are not collinear.

$& AB \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AB + BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;}\\& AB \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AB + BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;}\\& AB \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} && AB + BC \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;}$

What is the relationship between $AB + BC$ and $AC$? _________________

Write a conditional statement to express your conclusion:

If __________________ , then __________________

Feb 23, 2012

Aug 19, 2014