5. The historical society hired an artist to restore a stained glass window panel. After studying the original drawings, the artist knows that panel ABCD is square. He also knows that FG is a perpendicular bisector of BC and BC BE. However, in order to restore the panel to match its original specifications, he needs to know the measure of BED. Given: ABCD is a square FG BC BC BE Step 1: Draw EC on the diagram. Use the given information to explain how you know EGC EGB. Add the appropriate notation to the diagram. (5 points) Step 2: Building on the information from Step 1, use the spaces below to prove that mBEC = 60. Add the appropriate notation to the diagram. (5 points; 4 points for the proof, 1 point for the diagram) Statements 1. EGC EGB Reasons 1. Given 2. EB EC 3. Given 4. EB EC BC 5. mBEC = 60 Step 3: Next, use the spaces below to prove the measure of ECD = 30. Add the appropriate notation to the diagram. (5 points; 4 points for the proof, 1 point for the diagram) Given ABCD is a square : FG BC BC BE ECG EBG BEC is equilateral mBEC = 60 Prove mECD = 30 : Statements Reasons 1. BEC is equilateral 2. mGCE = 60 3. ABCD is a square 4. Substitution Step 4: Find mBED. Show your work and explain your reasoning. Add the appropriate notation to the diagram. (6 points; 4 points for showing work and explaining reasoning; 1 point for final answer; 1 point for diagram) Given: ABCD is a square FG BC BC BE ECG EBG BEC is equilateral mBEC = 60 ECD is isosceles Find: mBE D