Why is line AL equal to BC?

Because the point B is the center of the circle CGH, Definition 11 tells us that BC is equal to BG. next

---

Because D is the center of the circle GKL, DL is equal to DG. next

---

Since ADB is an equilateral triangle, DA and DB are equal . next

---

By axiom 3, the remainder AL is equal to the remainder BG. next

---

But BC is equal to BG, so AL is equal to BC by axiom 1. next

---

Therefore the straight line AL is equal to BC