\[ \begin{array}{l} \mathrm{AB}=4,9 \mathrm{~cm}, \quad \mathrm{AD}=8,5 \mathrm{~cm}, \quad \mathrm{AF}=11,8 \mathrm{~cm} \text { und } \mathrm{AH}=13,9 \mathrm{~cm} \\ \mathrm{AC}=5,4 \mathrm{~cm}, \quad \mathrm{AE}=9,4 \mathrm{~cm}, \quad \mathrm{AC}=13 \mathrm{~cm} \text { nnd } \mathrm{AJ}=15,3 \mathrm{~cm} \\ \mathrm{CB}=2,3 \mathrm{~cm}, \quad \mathrm{ED}=4 \mathrm{~cm}, \quad \mathrm{CF}=5,5 \mathrm{~cm} \text { and } \mathrm{cH}=6,4 \mathrm{~cm} \end{array} \] 1.1 Complete the similar triangles by writing the letters of the triangles in the carrect \( \triangle A B C||\mid \triangle \) \( \qquad \) III \( \Delta \) \( \qquad \) ||| \( \Delta \) \( \qquad \) 1.2 Why are the four triangles similar to each other?
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The similar triangles can be identified as \( \triangle A B C \sim \triangle A E D \sim \triangle A F G \sim \triangle A H J \). This means they maintain the same angles, which is a key characteristic of similar triangles! The four triangles are similar to each other because they all share a common angle at point A. This means that the angles remain the same across all triangles, and since the sides are proportional, they abide by the triangle similarity postulates (Angle-Angle or AA). So, as long as two angles are equal, the triangles will be similar, regardless of the lengths of the sides!
