when two perpendicular lines intersect, do they form four congruent angles?
Yes.
When two perpendicular lines intersect, they do indeed form four congruent angles. This is a fundamental property of perpendicular lines. To understand why, let me explain how you can arrive at this conclusion.
First, let's define perpendicular lines. Perpendicular lines are lines that intersect at a 90-degree angle (also known as a right angle). When two lines are perpendicular, each angle formed at the intersection is called a right angle.
To prove that these angles are congruent (meaning they have the same measure), we can use the properties of perpendicular lines. One property is that if two lines are perpendicular, the angles formed by any two intersecting lines are congruent or equal.
So, when the first perpendicular line intersects the second perpendicular line, it forms four angles: two acute (smaller than 90 degrees) and two obtuse (greater than 90 degrees) angles. Since all four angles are formed by the intersection of the two perpendicular lines, each angle is a right angle and therefore congruent to the others.
In conclusion, when two perpendicular lines intersect, they form four congruent angles, each measuring 90 degrees.