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\[ \begin{array}{l} \mathrm{AB}=4,9 \mathrm{~cm}, \quad \mathrm{AD}=8,5 \mathrm{~cm}, \quad \mathrm{AF}=11,8 \mathrm{~cm} \text { und } \mathrm{AH}=13,9 \mathrm{~cm} \\ \mathrm{AC}=5,4 \mathrm{~cm}, \quad \mathrm{AE}=9,4 \mathrm{~cm}, \quad \mathrm{AC}=13 \mathrm{~cm} \text { nnd } \mathrm{AJ}=15,3 \mathrm{~cm} \\ \mathrm{CB}=2,3 \mathrm{~cm}, \quad \mathrm{ED}=4 \mathrm{~cm}, \quad \mathrm{CF}=5,5 \mathrm{~cm} \text { and } \mathrm{cH}=6,4 \mathrm{~cm} \end{array} \] 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?

Ask by Daniels Christensen. in South Africa
Mar 16,2025

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\( \triangle ABC \sim \triangle ADE \sim \triangle AFG \sim \triangle AHJ \) These triangles are similar because the ratios of their corresponding sides are equal, and their corresponding angles are the same.

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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!

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