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. From the figure, we can observe: • AO = BO (indicated by the single tick marks on segments AO and BO). • CO = DO (indicated by the double tick marks on segments CO and DO). • AOC and BOD are vertically opposite angles. Step 2: Prove the congruence of AOC and BOD. Consider AOC and BOD: 1. AO = BO (Given from the figure) 2. AOC = BOD (Vertically opposite angles) 3. CO = DO (Given from the figure) By the Side-Angle-Side (SAS) congruence criterion, AOC BOD. Step 3: Deduce corresponding parts from the congruence of AOC and BOD. Since AOC BOD, their corresponding parts are equal: • AC = BD (Corresponding sides) • AD = AO + OD and BC = BO + OC. Since AO = BO and OD = OC, it follows that AD = BC. Step 4: Prove the congruence of ACD and BDC. Consider ACD and BDC: 1. AC = BD (Proven in Step 3) 2. CD = DC (Common side) 3. AD = BC (Proven in Step 3) By the Side-Side-Side (SSS) congruence criterion, ACD BDC. Step 5: Conclude the equality of corresponding angles. Since ACD BDC, their corresponding angles are equal. The angle ACD in ACD corresponds to the angle BDC in BDC. Therefore, ACD = BDC. This completes the proof. Proven that ACD = BDC