1. **Problem Statement:** We are given two triangles sharing a vertex with sides labeled 4 and 12 on the left triangle, and 2 and 6 on the right triangle. We need to determine which similarity shortcut applies: Hypotenuse-Leg (HL), Angle-Angle (AA), Side-Angle-Side (SAS), Side-Side-Side (SSS), or none. 2. **Recall similarity shortcuts:** - **AA:** Two angles of one triangle are congruent to two angles of another. - **SAS:** Two sides are proportional and the included angle is congruent. - **SSS:** All three sides are proportional. - **HL:** For right triangles, if the hypotenuse and one leg are proportional. 3. **Check side ratios:** - Left triangle sides: 4 and 12 - Right triangle sides: 2 and 6 Calculate ratios: $$\frac{4}{2} = 2$$ $$\frac{12}{6} = 2$$ Since both pairs of sides have the same ratio 2, the sides are proportional. 4. **Determine if the triangles are right triangles:** The problem mentions hypotenuse-leg as an option, implying right triangles. If these sides correspond to legs and hypotenuse, HL could apply. 5. **Conclusion:** Since two sides are proportional and the included angle is shared (the vertex where the triangles meet), the **SAS similarity** criterion applies. **Final answer:** SAS similarity shortcut.