Question

If false, prove a statement is false by providing a counterexample. If two lines intersect to form congruent angles, then the lines are perpendicular to each other.

1.True
2.False.

Answer 1

The statement is false; two lines can intersect to form congruent angles without being perpendicular. Additionally, perpendicular lines intersect to form 90° angles, not 270° angles.

Step-by-step explanation:

The statement "If two lines intersect to form congruent angles, then the lines are perpendicular to each other" is false. A counterexample is when two lines intersect to form congruent acute angles, such as 45° angles. In this case, the lines are not perpendicular even though they intersect to form congruent angles.

For example, imagine two lines intersecting at the center of an 'X'. If the angles formed at the intersection are all 45°, the lines are not perpendicular because perpendicular lines intersect to form a 90°, or right, angle.

Moreover, the statement "They are perpendicular, forming a 270° angle between each other" is also false because perpendicular lines intersect to form a 90° angle, not a 270° angle. A correct version of the statement would be: "If two lines are perpendicular, they form 90° angles with each other."

To illustrate this concept, think about the '+' sign. The lines forming a '+' are perpendicular and intersect to make equal 90° angles, not 270° angles.