Math Problem Statement
whats the right answer
Solution
The correct answer in the image is "The triangles are not similar because only two pairs of angles are congruent."
Explanation:
To determine if two triangles are similar, we use the AA (Angle-Angle) Similarity Postulate, which states that two triangles are similar if at least two angles in one triangle are congruent to two angles in the other triangle.
In this problem:
- Triangle has angles and (since the sum of a triangle's angles is ).
- Triangle has angles and .
Although and , the third angle does not match (). Therefore, the triangles are not similar, as not all three angles are proportionally congruent.
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Five Related Questions:
- What is the Angle-Angle (AA) postulate in triangle similarity?
- Can two triangles be similar if only one pair of angles is congruent?
- What are the differences between congruence and similarity in triangles?
- How do you calculate the missing angle in a triangle given the other two angles?
- Why is it important to ensure proportionality in sides for similarity beyond angles?
Tip:
Always sum the given angles to verify the third angle when dealing with triangle problems.
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Math Problem Analysis
Mathematical Concepts
Geometry
Triangle Similarity
Angle Properties
Formulas
Sum of angles in a triangle = 180°
Theorems
AA (Angle-Angle) Similarity Postulate
Suitable Grade Level
Grades 7-9