\[ \begin{array}{l} \mathrm{AB}=4,9 \mathrm{~cm}, \mathrm{AD}=8,5 \mathrm{~cm}, \mathrm{AF}=11,8 \mathrm{~cm} \text { and } \mathrm{AH}=13,9 \mathrm{~cm} \\ \mathrm{AC}=5,4 \mathrm{~cm}, \mathrm{AE}=9,4 \mathrm{~cm}, \mathrm{AG}=13 \mathrm{~cm} \text { and } \mathrm{AJ}=15,3 \mathrm{~cm} \\ \mathrm{CB}=2,3 \mathrm{~cm}, \mathrm{ED}=4 \mathrm{~cm}, \mathrm{GF}=5,5 \mathrm{~cm} \text { and } \mathrm{JH}=6,4 \mathrm{~cm} \end{array} \] 1.1 Complete the similar triangles by writing the letters of the triangles in the correct order. \[ \triangle A B C \text { ||| } \Delta_{ـ} \] 1.2 Why are the four triangles similar to each other? \( \qquad \) 1.3 Why is it important to write the letters in the correct order when it comes to similarity (2) \( \qquad \) \( \qquad \) Question 2 [13]
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The Deep Dive
The similar triangles in the first part can be denoted as follows: \[ \triangle ABC \text{ ||| } \triangle JHG \] This makes sense because the ratios of their corresponding sides match up, maintaining the proportionality that defines similar figures. The four triangles are similar to each other due to the Angle-Angle (AA) similarity criterion, which states that if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar. This means that regardless of their size, they maintain the same shape, allowing for proportional relationships between corresponding sides. When writing the letters in the correct order for similar triangles, it’s crucial because it establishes which vertices correspond to each other. This ensures that when you compare their sides, you are indeed looking at the correct parts of each triangle. Mislabeling can lead to incorrect conclusions about their similarity and proportional relations!