Angle Bisector Construction (GM: G-CO.D.12)
Click START to begin the angle bisection demo.
| Statement | Reason |
|---|---|
| 1. Segment AD ≅ Segment AE | Construction (Step 1): D and E are endpoints of the arc centered at A (radii of the same circle). |
| 2. Segment DF ≅ Segment EF | Construction (Steps 2 & 3): F is the intersection of two arcs with the exact same radius, centered at D and E. |
| 3. Segment AF ≅ Segment AF | Reflexive Property: AF is a common side shared by both △ADF and △AEF. |
| 4. △ADF ≅ △AEF | SSS Congruence Postulate: All three corresponding sides are congruent (Statements 1, 2, 3). |
| 5. ∠DAF ≅ ∠EAF | CPCTC: Corresponding Parts of Congruent Triangles are Congruent. |
| 6. Ray AF is the angle bisector of ∠BAC | Definition of Angle Bisector: The ray divides the angle into two congruent angles (Statement 5). |