Math Problem Statement

What is the value of Angle E in the given triangles based on AA similarity?

Solution

In the image provided, the video is discussing the concept of AA (Angle-Angle) similarity in triangles. Two triangles are shown, with information about the angles and side lengths.

Key Information:

  1. First Triangle (Triangle ABC):

    • A=110\angle A = 110^\circ
    • C=30\angle C = 30^\circ
    • By the triangle angle sum theorem (A+B+C=180\angle A + \angle B + \angle C = 180^\circ), we can calculate B\angle B.
    • B=18011030=40\angle B = 180^\circ - 110^\circ - 30^\circ = 40^\circ.
  2. Second Triangle (Triangle DEF):

    • D=110\angle D = 110^\circ (Given)
    • F=30\angle F = 30^\circ (Given)
    • To find E\angle E, we apply the same triangle angle sum theorem:
    • E=18011030=40\angle E = 180^\circ - 110^\circ - 30^\circ = 40^\circ.

Question Analysis (Multiple Choice):

  • What can we say about Angle E?
    • Since E\angle E is calculated as 40°, the correct answer is:
      • Angle E is 40 degrees.

Would you like any further clarification or details? Here are some additional related questions:

  1. How do we prove triangles are similar using the AA similarity criterion?
  2. What is the triangle angle sum theorem?
  3. How can you find the missing angle of a triangle if two angles are known?
  4. How does AA similarity help in comparing side lengths of triangles?
  5. What are the other similarity theorems (like SSS or SAS)?

Tip: In triangle problems, always apply the angle sum theorem to find unknown angles before proceeding with further comparisons or calculations.

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangle Similarity
AA Similarity

Formulas

Sum of angles in a triangle: A + B + C = 180°

Theorems

AA (Angle-Angle) Similarity Theorem
Triangle Angle Sum Theorem

Suitable Grade Level

Grades 7-10