To determine if the two triangles are similar, we need to check if their corresponding angles are equal and their corresponding sides are proportional.
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First, look closely: The image displays two right triangles, DEF and LJK. Both have a right angle marked (at D and L). We can see the side lengths for both triangles: Triangle DEF has sides 450 in, 600 in, and 750 in. Triangle LJK has sides 675 in, 900 in, and 1125 in. To prove similarity, we can check if the ratios of corresponding sides are equal.
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Next, find information: I will calculate the ratios of the corresponding sides of the two triangles. I will assume the sides correspond as follows based on their relative positions and the right angles: DE corresponds to LJ, DF corresponds to LK, and EF corresponds to JK.
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Then, review the findings:
- Ratio of DE to LJ: 450 / 675 = 2/3
- Ratio of DF to LK: 600 / 900 = 2/3
- Ratio of EF to JK: 750 / 1125 = 2/3
All three ratios are equal to 2/3. Since the corresponding sides are proportional and both triangles have a right angle (which means at least one pair of corresponding angles is equal), the triangles are similar by the Side-Side-Side (SSS) similarity criterion.
yes
Parent Tip: Review the logic above to help your child master the concept of similar triangles.
