Angles are equal in several specific geometric scenarios. Here's a breakdown:
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Vertically Opposite Angles: When two straight lines intersect, the angles opposite each other at the point of intersection are equal.
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Corresponding Angles: When a transversal intersects two parallel lines, the corresponding angles (angles in the same relative position at each intersection) are equal.
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Alternate Interior Angles: When a transversal intersects two parallel lines, the alternate interior angles (angles on opposite sides of the transversal and between the parallel lines) are equal.
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Alternate Exterior Angles: When a transversal intersects two parallel lines, the alternate exterior angles (angles on opposite sides of the transversal and outside the parallel lines) are equal.
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Angles Subtended by the Same Arc: In a circle, angles subtended by the same arc at the circumference are equal.
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Base Angles of an Isosceles Triangle: In an isosceles triangle, the angles opposite the equal sides (the base angles) are equal.
Here's a table summarizing this:
| Angle Type | Condition | Result |
|---|---|---|
| Vertically Opposite Angles | Intersecting lines | Equal angles are formed. |
| Corresponding Angles | Parallel lines intersected by a transversal | Equal angles are formed. |
| Alternate Interior Angles | Parallel lines intersected by a transversal | Equal angles are formed. |
| Alternate Exterior Angles | Parallel lines intersected by a transversal | Equal angles are formed. |
| Angles Subtended by Same Arc | Angles at circumference from same arc | Equal angles are formed. |
| Base Angles of Isosceles Triangle | Isosceles Triangle | Base angles are equal. |
In summary, angles are equal in specific relationships created by intersecting lines, parallel lines cut by a transversal, circles, and isosceles triangles.
