If line segment AB is perpendicular to CD, then ∠DCA is a right angle, and its measure is 90 degrees. Perpendicular lines form right angles at their point of intersection.
When line segment AB is perpendicular to CD, it implies that the two lines intersect to form a right angle at point C. The measure of ∠DCA is 90 degrees, as perpendicular lines create angles of this measure at their point of intersection.
In Euclidean geometry, a right angle is defined as exactly 90 degrees. Therefore, the relationship between the perpendicular lines AB and CD ensures that ∠DCA, the angle formed at the intersection, is a right angle with a measure of 90 degrees. This geometric property is fundamental in understanding the angles formed by intersecting lines in the plane.
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