write two conditional statements that make up the following biconditional statement: "Two lines are perpendicular if and only if their intersection creates 4 right angles."

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To recreate the biconditional statement "Two lines are perpendicular if and only if their intersection creates 4 right angles," we can break it down into two conditional statements:

1. If two lines are perpendicular, then their intersection creates 4 right angles.
2. If the intersection of two lines creates 4 right angles, then the lines are perpendicular.

Let's explain how to arrive at each conditional statement:

1. If two lines are perpendicular, then their intersection creates 4 right angles:
To determine if two lines are perpendicular, we need to check if the angle formed by their intersection is a right angle. We can use the concept of angles formed by intersecting lines to make this determination. If the angle is exactly 90 degrees, then we can conclude that the lines are perpendicular.

2. If the intersection of two lines creates 4 right angles, then the lines are perpendicular:
To establish that the lines are perpendicular, we need to confirm that their intersection forms four right angles. This means examining each of the four angles created by the intersection to determine if they are all right angles (90 degrees). If all four angles are right angles, then we can conclude that the lines are indeed perpendicular.

These two statements combined represent the biconditional relationship between perpendicular lines and the creation of 4 right angles at their intersection.

Conditional statement 1: "If two lines are perpendicular, then their intersection creates 4 right angles."

Conditional statement 2: "If the intersection of two lines creates 4 right angles, then the lines are perpendicular."