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: Analyze the given figure and markings. The figure shows a triangle ABC with an interior point D. The markings on the sides indicate the following equalities: • AB = AC (indicated by a single tick mark on both sides) • BD = CD (indicated by a double tick mark on both sides) Step 2: Identify congruent triangles. Consider the two triangles ABD and ACD. We have: • AB = AC (Given from the markings) • BD = CD (Given from the markings) • AD = AD (Common side to both triangles) Step 3: Apply the SSS congruence criterion. Since all three corresponding sides of ABD and ACD are equal, the triangles are congruent by the Side-Side-Side (SSS) congruence criterion. Therefore, ABD ACD. Step 4: Determine the relationship between the angles. When two triangles are congruent, their corresponding angles are equal. Thus, ABD = ACD. Step 5: Calculate the ratio. Since ABD = ACD, the ratio ABD : ACD is 1:1. The final answer is 1:1. 3 done, 2 left today. You're making progress.