Math Problem Statement
Solution
The task involves identifying which triangles are similar to the one given in the first image. Triangles are considered similar if their corresponding sides are proportional, meaning the ratios of corresponding side lengths are equal.
Let's compare the given triangle with the options:
The triangle in the first image has side lengths:
- 19 (left side)
- 20 (bottom side)
- 27 (right side)
To determine similarity, we will compare the ratios of corresponding sides for each of the four triangles in the second image:
-
For the top-left triangle (38, 10, 94.5):
- The ratio of sides for comparison would be:
- 38/19 = 2
- 10/20 = 0.5
- 94.5/27 = 3.5 Since these ratios are not equal, this triangle is not similar.
- The ratio of sides for comparison would be:
-
For the top-right triangle (70, 40.5, 19):
- The ratio of sides:
- 70/19 ≈ 3.68
- 40.5/20 = 2.025
- 19/27 ≈ 0.70 These ratios are also not equal, so this triangle is not similar.
- The ratio of sides:
-
For the bottom-left triangle (19, 10, 67.5):
- The ratio of sides:
- 19/19 = 1
- 10/20 = 0.5
- 67.5/27 = 2.5 The ratios are not equal, so this triangle is not similar.
- The ratio of sides:
-
For the bottom-right triangle (10, 81, 66.5):
- The ratio of sides:
- 10/19 ≈ 0.53
- 81/20 = 4.05
- 66.5/27 ≈ 2.47 These ratios are also unequal, meaning this triangle is not similar.
- The ratio of sides:
Based on the comparisons, none of the triangles in the second image are similar to the one shown in the first image.
Would you like further clarification on any of the steps or the reasoning behind this?
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Math Problem Analysis
Mathematical Concepts
Triangle similarity
Proportionality
Ratio comparison
Formulas
Ratio = Corresponding side of triangle A / Corresponding side of triangle B
Theorems
Triangle similarity theorem
Suitable Grade Level
Grades 8-10