Question
Question 13
10 pts
Which angle(s) is/are congruent?
Same Side Interior
Vertical
Alternate Exterior
Alternate Interior
Corresponding
10 pts
Same Side Interior
Vertical
Alternate Exterior
Alternate Interior
Corresponding
Ask by Munoz Valdez. in the United States
Jan 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Congruent Angles: Vertical, Alternate Exterior, Alternate Interior, Corresponding.
Not Congruent: Same Side Interior (they are supplementary).
Solution
To determine which angles are congruent among the given types—Same Side Interior, Vertical, Alternate Exterior, Alternate Interior, and Corresponding—we can analyze each based on the properties of angles formed by parallel lines intersected by a transversal.
-
Vertical Angles:
- Congruent. Vertically opposite angles are always equal in measure regardless of whether the lines are parallel.
-
Alternate Exterior Angles:
- Congruent if the lines are parallel. When two parallel lines are cut by a transversal, the alternate exterior angles are equal.
-
Alternate Interior Angles:
- Congruent if the lines are parallel. Similar to alternate exterior angles, alternate interior angles are equal when the lines are parallel.
-
Corresponding Angles:
- Congruent if the lines are parallel. Corresponding angles occupy the same relative position at each intersection where a transversal crosses the parallel lines and are hence equal.
-
Same Side Interior Angles:
- Not Congruent. Instead, these angles are supplementary (their measures add up to 180°) when the lines are parallel.
Summary:
- Congruent Angles: Vertical, Alternate Exterior, Alternate Interior, Corresponding.
- Not Congruent: Same Side Interior (they are supplementary).
Visual Representation:
(Replace the image link with an appropriate diagram if needed.)
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Beyond the Answer
Did you know that vertical angles, formed when two lines intersect, are always congruent? When two lines cross, they create pairs of opposite angles that measure the same, no matter what! Talk about a geometry rule that’s a crowd-pleaser!
In the world of parallel lines, corresponding angles are also congruent. Imagine two parallel lines cut by a transversal; each angle formed on one side has a buddy on the other side making the same angle! It’s like having an angle twin—always keeping it equal and stylish!
