This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Understand the definition of a perpendicular bisector. Given that l is the perpendicular bisector of line segment AB, it means that l intersects AB at its midpoint, let's call it M, and l is perpendicular to AB. Therefore, we have: • AM = MB (M is the midpoint of AB) • PMA = PMB = 90^ (l is perpendicular to AB) Step 2: Consider the triangles formed. Let P be any point on the line l. We need to show that P is equidistant from A and B, which means we need to prove that PA = PB. Consider the triangles PMA and PMB. Step 3: Prove the triangles are congruent. We can use the Side-Angle-Side (SAS) congruence criterion: • PM = PM (Common side to both triangles) • PMA = PMB = 90^ (From Step 1, definition of perpendicular bisector) • AM = MB (From Step 1, definition of perpendicular bisector) By SAS congruence criterion, PMA PMB. Step 4: Conclude that P is equidistant from A and B. Since PMA PMB, their corresponding parts are equal (CPCTC - Corresponding Parts of Congruent Triangles are Congruent). Therefore, PA = PB. This shows that any point P on the perpendicular bisector l is equidistant from points A and B. The final answer is PA = PB. Send me the next one 📸