Which of these gives enough information to determine whether two triangles are similar?
Understand the Problem
The question is asking which piece of information is sufficient to determine if two triangles are similar. It provides different options regarding the measurements known about the triangles.
Answer
D
Answer for screen readers
The correct choice is D: You know all 3 side lengths in each triangle.
Steps to Solve
- Understand Triangle Similarity Criteria
To determine if two triangles are similar, we need to apply the criteria for triangle similarity. The common criteria are Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS).
- Evaluate Option A
Option A states that you know the measure of 1 angle in each triangle. One pair of angles is not sufficient to establish similarity since at least two angles (AA) are required.
- Evaluate Option B
Option B states that you know 1 side length and 1 angle measure in each triangle. This option is also insufficient because knowing one side and one angle does not guarantee the other angle size, which is needed for similarity.
- Evaluate Option C
Option C states that you know 2 side lengths in each triangle. This alone is not sufficient, either, as we cannot conclude similarity without knowing the corresponding angles or the relationship of the third side.
- Evaluate Option D
Option D states that you know all 3 side lengths in each triangle. If all three sides in each triangle are proportional (using the Side-Side-Side similarity criterion), then this provides sufficient information to conclude that the triangles are similar.
The correct choice is D: You know all 3 side lengths in each triangle.
More Information
Knowing all three side lengths allows for comparison of the ratios between the sides of the two triangles. If the ratios of the corresponding sides are equal, the triangles are similar.
Tips
One common mistake is assuming that knowing only one angle or side is enough to establish similarity. Always check if the criteria (AA, SAS, SSS) are met for similarity.
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