Math Problem Statement
Solution
The diagram shows two parallel lines crossed by a transversal, forming eight angles. The given angle is , labeled as angle 3.
To identify all the angles congruent to this angle, we can use the following properties:
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Corresponding Angles: Angles in the same relative position at each intersection of the transversal and the parallel lines are congruent. Angle 3 corresponds to angle 7.
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Vertical Angles: Angles directly opposite each other when two lines intersect are congruent. Angle 3 is vertically opposite to angle 1.
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Alternate Interior Angles: Angles on opposite sides of the transversal but inside the two parallel lines are congruent. Angle 3 is alternate interior to angle 5.
Thus, the angles congruent to angle 3 are:
- Angle 1 (vertical angles)
- Angle 5 (alternate interior angles)
- Angle 7 (corresponding angles)
Let me know if you'd like further explanation or have any questions!
Here are 5 related questions for practice:
- Which angles are congruent to angle 2?
- What are the alternate exterior angles in this diagram?
- Which angle corresponds to angle 6?
- What are the properties of vertical angles?
- How do you identify supplementary angles in a transversal setup?
Tip: Always check for corresponding, alternate interior, and vertical angles when working with parallel lines and transversals.
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Math Problem Analysis
Mathematical Concepts
Parallel Lines
Transversal
Angle Congruence
Corresponding Angles
Vertical Angles
Alternate Interior Angles
Formulas
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Theorems
Corresponding Angles Postulate
Vertical Angles Theorem
Alternate Interior Angles Theorem
Suitable Grade Level
Grades 7-9