Big Ideas Math Geometry, 2014
BI
Big Ideas Math Geometry, 2014 View details
Chapter Review
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Exercise 1 Page 116

The conditional statement needs to be clarified before we can write the five conditionals.

See solution.

Practice makes perfect

We need to write the given statement as an if-then statement then write the converse, inverse, contrapositive, and bi-conditional statements. Let's start with the if-then statement.

If-Then

If-then statements take a specific form.

&If p, &then q.

Here, p is the hypothesis and q is the conclusion. For this exercise, we are told that "Two lines intersect in a point." Therefore, a logical if-them statement would be as follows.


&If two lines intersect, &then their intersection is a point.

Converse

When we write the converse, we swap the hypothesis and the conclusion.

&If two lines intersect at a point, &then the two lines intersect.

Inverse

When we write the inverse, we negate the hypothesis and conclusion in the original conditional statement.

&If two lines do not intersect, &then they do not intersect at a point.

Contrapositive

When we write the contrapositive, we negate the hypothesis and conclusion in the converse.

&If two lines do not intersect at a point, &then the two lines do not intersect.

Bi-Conditional

Bi-conditional statements use "if and only if" to show that a conditional statement works both ways. Since two lines will always form a point if they intersect, we can write the following bi-conditional statement.

&Two lines intersect, &if and only if their intersection is a point.