Statement

Reason

1. m(arc DB) = m(arc BE)

1. Given

2. ÐDAB @ ÐEAB

2. Inscr. Ðs intercepting @ arcs must be @

3. sAB is a diameter of ¤C

3. Given

4. ÐD is a rt. Ð

4. Ð inscr. in a semicircle

5. ÐE is a rt. Ð

5. "

6. ÐD @ ÐE

6. All rt. Ðs are @

7. sAB @ sAB

7. Reflexive

8. DDAB @ DEAB

8. AAS

9. sAD @ sAE

9. CPCTC
                                                     

II.

Statement

Reason

1. ÐEDC @ ÐB

1. Given

2. ÐC @ ÐC

2. Reflexive

3. ÐDEC @ ÐA

3. No-Choice Thm. (looking at third Ð of DEDC and of DABC)
                                                     

II. (alt.)

Statement

Reason

1. ÐEDC @ ÐB

1. Given

2. ÐC @ ÐC

2. Reflexive

3. DEDC ~ DABC

3. AA~

4. ÐDEC @ ÐA

4. Corresp. Ðs of similar Ds are @
                                                     

III.

Statement

Reason

1. sAB and sBC are tangent to ¤Q

1. Given

2. AD > DC

2. Given

3. sAB @ sCB

3. Tangents from an external pt. are @

4. sDB @ sDB

4. Reflexive

5. mÐABD > mÐDBC

5. Converse Hinge Thm. (or SSS¹); acceptable to say Hinge Thm.