Math Problem Statement

State if the two triangles are similar and justify the choice using similarity criteria.

Solution

The question asks if the two triangles are similar and provides four choices with different similarity criteria. Let’s analyze:

Observations:

  1. Given triangles: EDF\triangle EDF (bottom triangle) and BCA\triangle BCA (top triangle).
  2. Labeled angles:
    • Both triangles have a pair of marked congruent angles (E\angle E and B\angle B).
    • The shared bottom angle, labeled as F\angle F in EDF\triangle EDF and C\angle C in BCA\triangle BCA, is congruent because of the same marking.

Solution:

The AA (Angle-Angle) Similarity Criterion states that two triangles are similar if two angles in one triangle are congruent to two angles in another triangle. In this case:

  1. EB\angle E \cong \angle B (given),
  2. FC\angle F \cong \angle C (given).

Thus, by AA Similarity, EDFBCA\triangle EDF \sim \triangle BCA.

Correct Answer:

B) Yes; EDFBCA\triangle EDF \sim \triangle BCA by AA Similarity.


Do you want further clarification or details about triangle similarity?

Related Questions:

  1. What are the other similarity criteria for triangles besides AA?
  2. How does ASA (Angle-Side-Angle) similarity differ from AA similarity?
  3. Can we determine triangle similarity if only one pair of angles is known to be congruent?
  4. What are some examples of real-world problems involving similar triangles?
  5. How does similarity help in solving unknown side lengths in triangles?

Tip:

When determining triangle similarity, focus on the information provided about angles and side ratios—it's essential to identify the relevant criteria (AA, SSS, or SAS).

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangle Similarity

Formulas

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Theorems

AA (Angle-Angle) Similarity Theorem

Suitable Grade Level

Grades 8-10