Please Help Will give Brainliest to the Best Answers (75 points) --- 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 m∠BEC = 60°. Add the appropriate notation to the diagram. (5 points; 4 points for the proof, 1 point for the diagram) Statements Reasons 1. △EGC ≅ △EGB 1. Given 2. EB ≅ EC 3. Given 4. EB ≅ EC ≅ BC 5. m∠BEC = 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 m∠BEC = 60° Prove: m∠ECD = 30° Statements Reasons 1. △BEC is equilateral 2. m∠GCE = 60° 3. ABCD is a square 4. Substitution Step 4: Find m∠BED. 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 m∠BEC = 60° △ECD is isosceles Find: m∠BED

Statements                                                   Reasons

1. △EGC ≅ △EGB                                     1. Given

2. EB ≅ EC                                              Supposition

3. <EGC ≅ <EGB                                       Given

4. Equilateral  Triangle                       EB ≅ EC ≅ BC

5. Equilateral  Triangle                      m∠BEC = 60°

Statements                                                 Reasons

1. △BEC is equilateral                      AAS≅AAS postulate (angle angle side)

2. m∠ GCE = 60°                                   m∠ BEC = 60°  Equilateral Triangles

3. FG ⊥ BC &  FG ⊥ AD                                   ABCD is a square

4.  m∠ECD +  m∠ BEC = 30°+60°                           Substitution (right angles)

m∠DCG = 90°                                                  right angles of a square

m∠BED=   135°

Statements                                                   Reasons

1. △ECG ≅ △EBG                                             Given

2.  ABCD is a square                                       Given

3. BC ≅ BE                                                     Given

4. AB ≅ DC                                                   ABCD is a square

5.  m∠ABE ≅  m∠DCE                           Outside angles of congruent  

                                                               triangles △EGB≅      △EGC    

5.  △AEB≅ △DEC                         S.S.A ≅ S.S.A. ( side side angle) Postulate

△BEC is equilateral                                m∠BEC = 60°

△ECD is isosceles                                 m CD= mCE

∠ECD = 30°                                          m∠BEC = 60°

As m∠BEC +∠ECD = 30°+ 60°          right angle of the square ABCD

The equal sides of the isosceles triangles are called the legs and the unequal third side is called the base.

Angles opposite to the equal sides of the isosceles triangle must also be equal.

As the third angle is 30° so the other two angles must be 75° each to make a total of 180°.

m∠BED=  m∠BEC +  m∠CED

             = 60° + 75°= 135°

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could you give more information?