Math Problem Statement

Select the reason why these triangles are similar. If they are not, select 'Not similar.'

Solution

The two triangles shown in the image both have one angle marked as 5050^\circ, but there is no other information about the sides or the third angle.

To determine whether the triangles are similar, we can check the criteria for triangle similarity:

  1. AA (Angle-Angle) Similarity: If two angles in one triangle are congruent to two angles in another triangle, the triangles are similar.
  2. SSS (Side-Side-Side) Similarity: If all three sides of one triangle are proportional to the corresponding sides of another triangle, the triangles are similar.
  3. SAS (Side-Angle-Side) Similarity: If two sides of one triangle are proportional to two sides of another triangle and the included angle is congruent, the triangles are similar.

From the diagram, we only know one pair of angles (both marked as 5050^\circ), but there is no additional information about the other angles or sides. Based on this, there isn't enough information to use the AA, SSS, or SAS criteria. Therefore, the triangles cannot be confirmed as similar with the given data.

Thus, the correct answer is:

  • C. Not similar

Would you like a detailed explanation, or do you have any questions?

Here are 5 related questions to think about:

  1. How do we prove triangles are similar using the AA criterion?
  2. What is the difference between congruent and similar triangles?
  3. Can two triangles with one equal angle ever be similar?
  4. How do side ratios help in determining triangle similarity?
  5. What is the significance of the third angle in proving triangle similarity?

Tip: When solving similarity problems, always check for two corresponding angles or proportional side lengths for a conclusive result.

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Math Problem Analysis

Mathematical Concepts

Triangle Similarity
Angle-Angle (AA)
Side-Side-Side (SSS)
Side-Angle-Side (SAS)

Formulas

AA Similarity: Two pairs of angles are congruent.
SSS Similarity: Corresponding sides are proportional.
SAS Similarity: Two sides and the included angle are proportional and congruent.

Theorems

Triangle Similarity Theorem

Suitable Grade Level

Grades 8-10