Cricle Proof 2
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Given the circle below, where m⌢EB=m⌢DC and with lines ¯EC,¯BD,& ¯ED not drawn, prove that △EBD≅△DCE.
| Statement | Reason |
| 1.Draw lines ¯EC,¯DB,& ¯ED | 1.Two points define a line |
| 2. | 2.Given |
| 3.m∠EDB=12m⌢EB | 3. |
| 4.m∠CED=12m⌢CD | 4.Measure of inscribed angle is 1/2 the measure of intercepted arc |
| 5.12m⌢EB=12m⌢DC | 5. |
| 6. | 6.Substitution Property of Equality |
| 7.∠EDB≅∠CED | 7.Definition of congruent angles |
| 8.∠EBD≅∠ECD | 8. |
| 9.¯ED≅¯ED | 9.Reflexive Property |
| 10.△EBD≅△DCE | 10. |
A.
What is the missing statement in step 2?
- Draw center O
- m⌢EB=m⌢DC
- △EBD≅△DCE
- ¯EB≅¯DC
B.
What is the missing reason in step 3?
- Measure of central angle is 1/2 the measure of intercepted arc
- Intersecting Secant Theorem
- Sum of the angles in a triangle is half of the sum of the non-overlapping central angles in a circle
- Measure of inscribed angle is 1/2 the measure of intercepted arc
C.
What is the missing reason in step 5?
- Multiplicative Identity Property
- Multiplicative Inverse Property
- Multiplicative Property of Equality
- Closure Property of Multiplication
D.
What is the missing statement in step 6?
- m∠EDB=m∠CED
- m∠EDB=12m∠CED
- m∠CED=m⌢EB
- m⌢EB=12m⌢CD
E.
What is the missing reason in step 8?
- Implied by diagram
- Intersecting chords create congruent angles
- All inscribed angles of the same circle are congruent
- Inscribed angles intercepting the same arc are congruent
F.
What is the missing reason in step 10?
- SSA
- AAS
- SSS
- AAA