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: Identify the given information from the figure and the problem statement. From the problem statement, we are given that AB = AC. From the figure, we can observe: • AB = AC (indicated by the tick marks on sides AB and AC). • BM = MC (indicated by the tick marks on segments BM and MC). • AM is a common side to both AMB and AMC. Step 2: Prove the congruence of AMB and AMC. Consider AMB and AMC: 1. AB = AC (Given) 2. BM = MC (Given from the figure) 3. AM = AM (Common side) By the Side-Side-Side (SSS) congruence criterion, AMB AMC. Step 3: Conclude the equality of corresponding angles. Since AMB AMC, their corresponding angles are equal. Therefore, AMB = AMC. Step 4: Use the property of angles on a straight line. Angles AMB and AMC form a linear pair on the straight line BC. The sum of angles in a linear pair is 180^. AMB + AMC = 180^ Step 5: Calculate the measure of the angles. Since AMB = AMC, we can substitute AMB for AMC: AMB + AMB = 180^ 2 AMB = 180^ AMB = (180^)/(2) AMB = 90^ Since AMB = AMC, it follows that AMC = 90^. Therefore, BMA = CMA = 90^. Proven that BMA = CMA = 90^